Sensor comprising a photovoltaic device

ABSTRACT

In one example, a sensor comprises a photovoltaic device. The photovoltaic device comprises a core having a shape that is at least partially spherical, an absorber disposed over the core, and a transparent conductor disposed over the absorber. Other examples and related methods are also disclosed herein.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation-in-part of U.S. applicationSer. No. 14/170,007 filed Jan. 31, 2014 which in turn claims the benefitof U.S. Provisional Application No. 61/760,127 filed Feb. 3, 2013. SaidApplication No. 61/760,127 and said application Ser. No. 14/170,007 arehereby incorporated by reference herein in their entireties.

BACKGROUND

Photovoltaic devices are typically used in solar panels having a planarstructure. The power output of a planar device, however, decreasesincreasingly oblique angles of the incident light rays. As a result,solar panels having planar photovoltaic devices may not be deployed athigher latitudes since the decreased power output may not justify theexpense of the solar panel. In addition, the amount of power generatedover a day from sunrise to sunset may not be sufficient to justify theexpense of the solar panel system due to decreased power output in theearly morning or late evening. Solar trackers could be used to directthe planar device solar panel to track the movement of the sun over thecourse of a day, and to compensate for altitude and seasonal anglechanges of the sun, but such solar trackers may be too complex and costprohibitive for widespread deployment. Furthermore, planar photovoltaicdevices have had generally limited efficiencies which also has impededwide scale deployment of solar panel systems.

DESCRIPTION OF THE DRAWING FIGURES

Claimed subject matter is particularly pointed out and distinctlyclaimed in the concluding portion of the specification. Such subject,however, matter may be understood by reference to the following detaileddescription when read with the accompanying drawings.

FIG. 1 is diagram of a solar power system comprising an array ofphotovoltaic devices referred to as a pleniron in accordance with one ormore embodiments.

FIG. 2 is a diagram of a pleniron photovoltaic device in accordance withone or more embodiments.

FIG. 3 is a diagram of another pleniron photovoltaic device inaccordance with one or more embodiments.

FIG. 4 is a diagram of yet another pleniron photovoltaic device inaccordance with one or more embodiments.

FIG. 5 is a diagram of an alternative pleniron photovoltaic device inaccordance with one or more embodiments.

FIG. 6 and FIG. 7 are diagrams illustrating structural proportions of anexample pleniron 200 and its components in accordance with one or moreembodiments.

FIG. 8 is a diagram of an example ray trace illustration of totalinternal reflection in the absorber layers of an example pleniron with adegenerate semiconductor or conductive interior in accordance with oneor more embodiments.

FIG. 9 is a diagram of a single, monochromatic plane wave thattransforms in the wave guiding surfaces on all sides of the absorber ofan example pleniron, to a resonant multi-modal resonance in accordancewith one or more embodiments.

FIG. 10 is a diagram illustrating an example of the density of statesfor a planar photovoltaic device for comparison to a plenironphotovoltaic device in accordance with one or more embodiments.

FIG. 11 is a diagram illustrating the density of states for a plenironphotovoltaic device in accordance with one or more embodiments.

FIG. 12 is a graph of voltage versus junction depth of an examplepleniron in accordance with one or more embodiments.

FIG. 13 , FIG. 14 , FIG. 15 , FIG. 16 and FIG. 17 are graphs andillustrations of charge density in an example pleniron in accordancewith one or more embodiments.

FIG. 18 is an example diagram of the energy band diagram for crystallinesilicon, an indirect band gap semiconductor, for analysis of use in anexample pleniron in accordance with one or more embodiments.

FIG. 19 is a diagram of the plotted Fermi distribution for a Fermienergy of 2 eV and 300 K temperature where the vertical axis is thenumber of electrons in the state with the energy on the horizontal axisfor an example pleniron in accordance with one or more embodiments.

FIG. 20 is a graph of Fermi Equilibrium distribution with hot electronperturbation in a pleniron in accordance with one or more embodiments.

FIG. 21 is an illustration of two graphs showing transmissionprobability by angle of incidence for Sigma and Pi polarizations,respectively, for a pleniron in accordance with one or more embodiments.

FIG. 22 is a diagram of an example array of plenirons having anarrangement of the plenirons with defined coordinates wherein theplenirons are not shadowing each other over a widest possible range ofincident angles of light rays from the sun in accordance with one ormore embodiments.

FIG. 23 is a diagram of an example array of plenirons taken at anextreme angle as would be viewable from the viewpoint of the sun at anextreme evening or early morning position in accordance with one or moreembodiments.

FIG. 24 is an array of plenirons at the same extreme angle as the arrayof FIG. 23 but with the φ angle rotated by π/6 radians in accordancewith one or more embodiments.

FIG. 25 is a plot of a solution for the power output of an example arrayof plenirons relating the Phi to the Theta with the vertical axis beingpower in watts and the two horizontal axes being the Theta and the Phi,respectively, in accordance with one or more embodiments.

FIG. 26 is a diagram showing geometrical and differential analysis ofshadowing angles for the angle ϕ in accordance with one or moreembodiments.

FIG. 27 is a diagram showing geometrical and differential analysis ofshadowing for the angles θ and ϕ in accordance with one or moreembodiments.

FIG. 28A is a diagram clarifying the nearest neighbor distance, a, inthe same top view, and also showing α for a hexagonal pleniron arraytype in accordance with one or more embodiments.

FIG. 28B is a diagram showing the coordinate formalism for the angle ϕin an isometric view and including the plenirons as wireframes of theirouter shell in accordance with one or more embodiments.

FIGS. 29A and 29B are diagrams illustrating the subject matter of FIG.28A and FIG. 28B for a rectangular pleniron lattice arrangement naccordance with one or more embodiments.

FIG. 30A is a diagram of an isometric wireframe view of two separatephoton packets in accordance with one or more embodiments.

FIG. 30B is a diagram illustrating a cross-section in the plane ofincidence of light rays in accordance with one or more embodiments.

FIG. 31 is a diagram of a plenistell array made such that each plenironis individually addressed with a matrix of vias and lateral conductorlines in separate electrically isolated lines in accordance with one ormore embodiments.

FIG. 32 is a diagram of a Gaussian, point, or plane wave sourcetranslating in either a line or more complex orbit relative to aplenistell detector array in accordance with one or more embodiments.

FIG. 33 is a diagram of a Gaussian-shaped pleniron created as a resultof a topographical back contact with a conducive imprinting process inaccordance with one or more embodiments.

FIG. 34 is a diagram of a pleniron of an approximately spheroidal toinverted-parabolic outer shape in two separate cross-sections inaccordance with one or more embodiments.

FIG. 35 is a diagram of a plenistell with light capturing plenirons witheither transparent or semi-transparent bottoms or bases in accordancewith one or more embodiments.

FIG. 36 is a diagram of flat waveguide that is flexible and turnedaround to the other side of an object in accordance with one or moreembodiments.

It will be appreciated that for simplicity and/or clarity ofillustration, elements illustrated in the figures have not necessarilybeen drawn to scale. For example, the dimensions of some of the elementsmay be exaggerated relative to other elements for clarity. Further, ifconsidered appropriate, reference numerals have been repeated among thefigures to indicate corresponding and/or analogous elements.

DETAILED DESCRIPTION

In the following detailed description, numerous specific details are setforth to provide a thorough understanding of claimed subject matter.However, it will be understood by those skilled in the art that claimedsubject matter may be practiced without these specific details. In otherinstances, well-known methods, procedures, components and/or circuitshave not been described in detail.

In the following description and/or claims, the terms coupled and/orconnected, along with their derivatives, may be used. In particularembodiments, connected may be used to indicate that two or more elementsare in direct physical and/or electrical contact with each other.Coupled may mean that two or more elements are in direct physical and/orelectrical contact. However, coupled may also mean that two or moreelements may not be in direct contact with each other, but yet may stillcooperate and/or interact with each other. For example, “coupled” maymean that two or more elements do not contact each other but areindirectly joined together via another element or intermediate elements.Finally, the terms “on,” “overlying,” and “over” may be used in thefollowing description and claims. “On,” “overlying,” and “over” may beused to indicate that two or more elements are in direct physicalcontact with each other. However, “over” may also mean that two or moreelements are not in direct contact with each other. For example, “over”may mean that one element is above another element but not contact eachother and may have another element or elements in between the twoelements. Furthermore, the term “and/or” may mean “and”, it may mean“or”, it may mean “exclusive-or”, it may mean “one”, it may mean “some,but not all”, it may mean “neither”, and/or it may mean “both”, althoughthe scope of claimed subject matter is not limited in this respect. Inthe following description and/or claims, the terms “comprise” and“include,” along with their derivatives, may be used and are intended assynonyms for each other.

Referring now to FIG. 1 , a diagram of a solar power system comprisingan array of photovoltaic devices referred to as a pleniron in accordancewith one or more embodiments will be discussed. In FIG. 1 , an examplesolar power system 100 may comprise an array 110 of photovoltaicdevices, referred to herein as a “pleniron”. A pleniron may refer to aphotovoltaic device having a general spherical or spheroidal shape orstructure, wholly or in part, that is capable of generating electricalpower in response to photo energy impinging thereon. plenironphotovoltaic devices with particular structures and properties are shownin and described herein with particular detail as discussed, below. Apleniron array 110 may comprise one or more pleniron photovoltaicdevices arranged in a regular or irregular pattern to receive incidentlight rays 120 from a light source, typically the sun 118, to generateelectrical power. Deployed as part of solar power system 100, plenironarray 110 may generate direct current (dc) power 112 that optionally maybe converted to alternating current (ac) power 116 via a power inverter114, although the scope of the claimed subject matter is not limited inthis respect. A first example of a pleniron photovoltaic device is shownin and described with respect to FIG. 2 , below.

Referring now to FIG. 2 , a diagram of a pleniron photovoltaic device inaccordance with one or more embodiments will be discussed. As shown inFIG. 2 , one example of a pleniron 200 may comprise a pleniron core 210formed on or in a substrate 212 which typically may comprise asemiconductor material such as silicon Gallium Arsenide, CadmiumTelluride, polycrystalline silicon, or the like. The pleniron core 210may comprise a generally spherical or spheroidal structure, wholly or inpart and may comprise monocrystalline silicon in one or moreembodiments. A photovoltaic semiconductor layer 216 may be disposed onsubstrate 212 and at least partially surrounding pleniron core 210 asshown to function as an absorber 208. Semiconductor layer 216 maycomprise an N doped or P doped semiconductor such as silicon. Atransparent conductive oxide (TCO) layer 218 may be formed onsemiconductor layer 216 in order to provide properties of opticaltransparence and electrical conductivity. Example materials for TCOlayer 218 may include Aluminum doped zinc oxide (AZnO), tin doped zincoxide (SnZnO), boron doped zinc oxide (BZnO), indium tin oxide (ITO),and so on, and the scope of the claimed subject matter is not limited inthis respect.

In one or more embodiments, as shown in FIG. 1 , a back contact layer214 may be disposed between the semiconductor layer 216 and thesubstrate 212 wherein the back contact layer 214 may comprise anoptically transparent conductor such as a transparent conductive oxide(TCO) similar to the TCO layer 218. The material external to TCO layer220 may comprise an encapsulant 220 for example air where TCO layer 218is the outermost layer of pleniron 200, or alternatively a transparentor low index coating or filler, and the scope of the claimed subjectmatter is not limited in these respects. Details of the operation ofpleniron 200 will be discussed in further detail from FIG. 6 onward,below.

In one or more embodiments, a pleniron 200 is a unit cell of an overallphotovoltaic or photoactive or photo-generative device that, althoughnot exactly identical, is generally congruent with other plenirons 200in the device. A plenistell may refer to the overall device composed ofmultiple plenirons 200 and may comprise an array 110 of plenirons 200 inthree dimensions that are randomly or regularly spaced. If regularlyspaced, Cartesian, polar, or spherical coordinates may be used todescribe the pleniron 200 unit cell Basis vector set to define an arrayor lattice.

A pleniron core 210, in one or more embodiments may be a semiconductormaterial, of either N or P type (or intrinsic), or a degeneratesemiconductor, or a conductive metallic material, that is physicallyshaped to optimize optical and electronic performance of the overalldevice. Typical semiconductor materials might be crystalline silicon(c-Si), polysilicon (p-Si), nanocrystalline silicon (nc-Si), CadmiumTelluride (CdTe), Cadmium Sulfide (CdS), Gallium Arsenide (GaAs),Silicon Carbide (SiC), Gallium Nitride (GaN), or any othersemiconducting material. A pleniron core 210 in other embodiments may bea semi-pseudo spherical smoothed granular piece of degeneratesemiconductor or metallic material, of the correct proportions to thematerial system as discussed herein that, when layered with the correctproportions of thin film semiconductors and a transparent conductor,will exhibit the optical volume phenomena outlined in other sections ofthis document. Such other embodiments may also involve the use of anytype of back-substrate structuring, such as nano-imprinting ormicro-imprinting in polymers or otherwise, followed by plating,radio-frequency (RF) or direct-current (dc) sputtering or chemical vapordeposition (CVD) applied conductors to obtain a 3D pseudo sphericalarray surface. Layering of the correct proportions of semiconductors onthis background, along with a transparent conductor, will allow theappropriate optical volume to occur.

In one or more embodiments, a pleniron 200 may have a shape in physical3-D space, with surface peaks and valleys less than 1/10 of thewavelength of light of interest dependent on material energy band gap,to avoid random roughness that will scatter incident photons. Ingeneral, the pleniron 200 surfaces including various layers and core 210may be smooth and curved in definable proportions to the core 210. Thecurvature may vary over distances comparable to an upper limit of about25% of the diameter, although the scope of the claimed subject matter isnot limited in these respects.

A pleniron core 210 and the layers of the pleniron 200 may have varyingcurvatures with the underlying purpose of lensing light into the innercore 210. The proportions of layer thicknesses in relation to the innercore will maintain a ratio critical to maximizing Total InternalReflection (TIR) in the inner core absorber material only. It is not asdesirable to obtain TIR in outer layers, but to minimize the number ofpasses of incident photons through the outer layers, preferably to onlyone, and maximize the passes on the interior of the absorbing core.

In one or more embodiments, the general shape of the pleniron 200, if itmeets the above parameters, in conjunction with other electronicparameters discussed herein, may be described as any of the following:roughly spherical, ovoidal, multi-lobed ovoidal, elliptical, lobedelliptical, dipolar modal, multi-polar modal, and so on. Radialvariations could, dependent on the average radius, be up to about 20-25%of the average.

In one or more embodiments, the size of the pleniron, as describedabove, may be determined by the average size dimension of the core 210,and the proportionality of thicknesses of the upper/outer layers. Thecore size is largely determined by electronic aspect factors, such asmaterial system (semiconductor N and P type) and the doping level. Inaddition, the core size may determine the thicknesses of the filmsdeposited on top of the cores, due to the proportionality considerationsto be detailed in the following document. These proportionalityconsiderations come out of optics, the lensing and guiding of light inthe appropriate spectrum of interest, for example visible and infrared(IR) light, such that an incident photon plane wave may be virtually100% concentrated, retained, and guided into absorber material over avirtual optical thickness of the device.

In one or more embodiments, from an optical standpoint, for transmissioninto the pleniron core 210, or layers above a conductive or degeneratesemiconductor pleniron core 210, it is possible to obtain an increase inthe number of wave modes and their corresponding amplitude (density ofphoton states), and to encapsulate the pleniron devices in an opticallydense material, such as glass. Although refracted rays may be moretoward normal incidence for all incidence air-angles, the transmissionprobabilities of incident rays may be increased across all incidentangles such that trapping may be easier to achieve with largergeometries. This is also detailed as a result of a fundamental equation,Equation 1 listed below, by changing the incident medium index ofrefraction to a value commensurate with the encapsulation material. Theangles or incidence on the pleniron device, and therefore the plenistellarray 110 as a whole, are altered by the Snell's law incidence of thesolar radiation at the interface between the encapsulant and the air.

In accordance with the foregoing, pleniron 200 photovoltaic device mayallow the use of reverse construction of the device such that theencapsulant itself may be patterned, whether it be glass or transparentpolymer or otherwise, and the semiconductor materials, and subsequenttransparent conductor, may be deposited after into the absences affordedby the patterning. With pseudo-sphere or multi-modal pleniron cores 210,this absence patterning are essentially conformally depositing layers oftop contact, semiconductor junction, and back contact in a superstraterather than a substrate configuration. Pleniron 200 construction,therefore, is not limited to a substrate configuration to obtain opticalvolume phenomena, but may be achieved by a variety of different processmethodologies.

Referring now to FIG. 3 , a diagram of another pleniron photovoltaicdevice in accordance with one or more embodiments will be discussed.pleniron 200 of FIG. 3 is substantially similar to the structure ofpleniron 200 of FIG. 2 with the addition in the absorber 208 ofsemiconductor layer 222 having opposite doping or charge properties withrespect to semiconductor layer 216. For example, if semiconductor layer216 is a P type semiconductor, then semiconductor layer 222 is an N typesemiconductor. Alternatively, if semiconductor layer 216 is an N typesemiconductor, then semiconductor layer 222 is a P type semiconductor.

Referring now to FIG. 4 , a diagram of yet another pleniron photovoltaicdevice in accordance with one or more embodiments will be discussed.pleniron 200 of FIG. 4 is substantially similar to the structure ofpleniron 200 of FIG. 3 with the addition in the absorber 208 of anintrinsic layer 224 disposed between semiconductor layer 216 andsemiconductor layer 222. Intrinsic layer 224 may be more lightly dopedthan either of semiconductor layer 216 and/or semiconductor layer 222.Utilization of intrinsic layer 224 may result in a PIN diode or an NIPdiode structure for pleniron 200 suitable for photovoltaic operation,although the scope of the claimed subject matter is not limited in thisrespect.

Referring now to FIG. 5 , a diagram of an alternative plenironphotovoltaic device in accordance with one or more embodiments will bediscussed. pleniron of FIG. 5 is substantially similar to pleniron 200of FIG. 2 except that instead of having a separate pleniron core 210, astructure 510 having the same or nearly the same function and propertiesof a pleniron core 210 may be formed using the material of substrate 212such that structure 510 has a spherical or partially spherical shape, ora spheroidal or partially spheroidal shape as shown. Furthermore, apleniron 200 as shown in any of FIG. 2 , FIG. 3 of FIG. 4 , and so on,may be formed with structure 510 to function as a pleniron core 210rather than utilizing a separate material or structure for pleniron core210. In general, any shape similar to pleniron core 210 may be formedvia any semiconductor manufacturing process to result in the same orsimilar properties for pleniron 200, for example spheres, domes, bumps,bubbles, and so on, and the scope of the claimed subject matter is notlimited in this respect. The operation and function of a pleniron 200are discussed in further detail, below.

Referring now to FIG. 6 and FIG. 7 , proportions of a pleniron 200 andis component structures in accordance with one or more embodiments willbe discussed. As pleniron 200 may refer to a photovoltaic device thatcan be assembled into an array, module, or overall device to utilizebroad spectrum electromagnetic radiation to produce electrical power.Such a device may comprise a plurality of plenirons 200, a unit devicethat may be arranged into regular or irregular spaced array formats suchas array 110 of FIG. 1 to make electrical power from incident photonsfrom a light source such as the sun 118. The pleniron 200 may beconsidered as a basic unit device that can produce power. The assemblyof multiple plenirons into the aforementioned array may be synergisticin its production of electrical power. A pleniron based device may beoptimized for a solar power system 100 to capture of incident photonsusing optical dielectric properties in selected proportions including,but not limited to, material thicknesses, pleniron core size, opticalindices of refraction, and optical attenuation coefficients. pleniron200 uses optical proportionality to provide a desired electromagneticwave, Total Internal Reflection (TIR) properties to trap incident lightand to prevent reflection and re-emission of captured photons. In one ormore embodiments, the layer proportionality of pleniron 200 may adhereto the following function:

$\sin^{- 1}\left( \frac{n_{2}R_{c}}{n_{1}\left( {d_{2} + d_{3} + R_{c}} \right)} \right)$

In the above function, n2 is the index of refraction of a TransparentConductive Oxide (TCO) layer 218 as the outer layer of the pleniron, n1is the index of refraction of the material 220 outside the TCO 218,usually air or a low index filler, d_(A) is the thickness of theabsorber 208, in this case the N-doped or P-doped semiconductor layer216, over pleniron core material 210, d_(TCO) is the thickness of theTCO layer 218, and the R_(c) is the diameter of the underlying plenironcore 210. FIG. 6 shows these proportions of pleniron 200 incross-section.

A mathematical expression that relates the angle, θ, of a ray of light120 from a point source such as the sun 118 to the refracted ray insideof an optically dense material providing the angle relative to a radialray from the center of the pleniron core 210 is shown, below. Likewise,the same expression also may be used to determine the refracted angle ina material with arbitrary index, incident from a larger radius materialwith a different arbitrary index:

$\begin{matrix}{\theta_{in} = {\sin^{- 1}\left( \frac{n_{1}{\sin\left( \theta_{1} \right)}\left( {d_{2} + d_{3} + R_{C}} \right)}{n_{2}\left( {d_{3} + R_{C}} \right)} \right)}} & {{Eqn}1}\end{matrix}$

The variables of Equation 1 are the same as listed, above, for pleniron200. The following expression provides the minimum angle of incidence,from air 222, or whatever other material, that the light from the sourceis incident from, encapsulant polymer, and so on, into the transparentconductor layer 218 over the semiconductor layer 216 and/orsemiconductor layer 222 to provide total internal reflection inside ofthe transparent conductor layer 218 alone. While this traps the lightwithin the structure, it does not guarantee light is trapped uniquely inthe absorber 208. The results leading to Equation 1 ensure that:

$\theta_{{Min}({{air} - {TCO}})} = {\sin^{- 1}\left( \frac{d_{TCO} + R_{C}}{d_{A} + d_{TCO} + R_{C}} \right)}$

The mathematics leading to these expressions were derived from opticalphysics and first principles using, in part, geometric and trigonometricanalysis similar to that obtained from FIG. 7 . Note that the relationsprovided above allow derivation of the subsequent angles of each ray,even viewed as wave phenomena, from one layer to another, to allow thedetermination of critical limiting angles that provide nearly completelight trapping. Such is the outcome of Equation 1. It should be notedthat, with the decreasing radii of each subsequent layer, and theincreasing index off refraction of each layer inward, the probability oflight trapping increases far faster than a planar photovoltaic devicecould achieve. This is understandable easily from the illustrationabove, by noting that, due to the curved surfaces, the light ray nearthe angle marked θ₃ to the interface to that marked θ₄ is longer thanthat which would otherwise impinge on the perpendicular line in the TCOlayer 218, which would of course occur in a planar cell, thereby makingmore oblique the angle of incidence onto the surface of semiconductorlayer 216. It is precisely this slightly added path length, onto acurved geometry, which provides the design of pleniron 200 with thepotential to guide light and trap it without loss, or nearly withoutloss. The more oblique angle onto the underlying layer decreases thechances of a re-transmission out of the structure once it is transmittedinto underlying layers.

Referring now to FIG. 8 , an example ray trace illustration of totalinternal reflection in the absorber layers of a pleniron 200 with adegenerate or conductive interior will be discussed. A pleniron 200 mayimplement Optical Volume principles, where the device acts as ameta-material that is both absorptive and transparent. As shown in FIG.8 , due to the proportionality, light is trapped by Total InternalReflection, similarly to lens design principles, and is attenuated atthe point of entry in the 3-dimensional device. The layers act asoptical waveguide resonators to concentrate light in the X-Y plane,parallel to the underlying substrate 212, but homogeneously distributethe Density of photon states in the z-direction, the optical depth ofthe device perpendicular to the X-Y substrate plane.

Referring now to FIG. 9 , a single, monochromatic plane wave thattransforms in the wave guiding surfaces on all sides of the absorber208, to a resonant multi-modal resonance will be discussed. A pleniron200 may utilize optical depth, wherein the optical indices andthicknesses of the device layers capture and retain electromagneticradiation at broad band wavelengths, for example approximately 300nanometers (nm) to 1100 nm depending on material system chosen by themanufacture. In so doing, a pleniron 200 is able to utilize the entirevolume of pseudo-absorber 208 material, the optical depth of the device,such that the number of photons in the device at an instantaneousmoment, t, is increased.

In one or more embodiments the pleniron 200 may be optimized for Opticaldensity of photon states spatial homogeneity through the concentrationof light in axes parallel to the underlying substrate 212, andpropagation of light, from the points of light entry, in the verticaldirection, perpendicular to the substrate 212. Although propagation inspherical, multimodal, or curved granular-based annular waveguides willbe in all three coordinate directions, once trapped within the layersand core of the device, it is the vertical direction orthogonalizedwhich provides an optical thickness without corresponding attenuation.For these reasons an array 110 of plenirons 200, referred to herein as aplenistell, is a meta-material since it has synergistic properties thatmay be difficult if not impossible to achieve from bulk materials. Sincethe optical thickness is expanded such a plenistell meta-material may beregarded as transparent, to its full depth, and absorptivesimultaneously.

The optical trapping and retaining structure for an example pleniron 200as described herein may include smooth interfaces between vacuum/air,window-layer conductive oxides, semiconductor layers, core materials,and back electrical contacts and reflectors. The option for smoothness,in general, is that the peak to peak features are spaced closer than thewavelength of light in the material, referred to as λ, in vacuum dividedby index of refraction of the material, divided by ten. This issummarized in the below equation:

$\begin{matrix}{d < \frac{\lambda}{10*n}} & {{Eqn}2}\end{matrix}$

In the embodiment discussed, above, varying degrees of roughness,deviating from that shown in FIG. 9 may provide performance at a reducedvalue from the optimum. Non-optimum roughness values will provideadvantage in optical volume enhanced density of states homogeneity,although performance will degrade by a factor of at least d{circumflexover ( )}2 as roughness increases. In addition, the peak to peak value,may be appended by a peak to valley distance such that the averagesurface deviation angle be less than or equal to about 8 degrees. Suchan arrangement may encompass values in excess of this, although theperformance of the cell may degrade by a factor of at least thefollowing with increased deviation angle:

ΔP=sec²(θ)

In one or more embodiments, pleniron 200 may be considered a lighttrapping, retention, and/or processing optimization device that involvesthe exterior vacuum or air to transparent conductive oxide interfacebeing comparably thick to the underlying semiconductor layer 216 whereinlight incidence from virtually all angles may not be of grazingincidence and retransmission within the TCO 218, nor grazing incidenceand infinite TIR retention within the TCO. This involves opticaloptimization such that the semiconductor layers and core, of knownindices of refraction as a function of wavelength—dispersion relation,accept and retain the electromagnetic radiation. In such an embodiment,the TCO 218 to absorber 208 thickness, with most semiconductor and TCOmaterials, be of ratio of about 1 to about 1.5, that is the ratio of thethickness of the TCO 218 to the absorber 208. Ratios within about plusor minus 50% of this value may still function.

In one or more embodiments, pleniron 200 utilizes the optically tunedwaveguide volumes, whether annular or optical resonators, for opticalpath length for attenuation and exciton generation. This length isdifferent from a planar device vertical or scattered optical path lengthsince all levels of the device can be reached by un-attenuated lightbefore entry into the device occurs. To take full advantage of allincident angles, and full optical volume, the plenirons 200 in an array110 should not shadow each other significantly. Mitigation of shadowingmay be considered an optimum wherein the spacing of the plenirons 200 inthe array 110 are spaced such that their bases do not occlude each otherby more than about 20% at the most open viewpoint. For example, if thecompleted plenirons 200 were about two microns in radius each, center tocenter spacing would be no more than about 7.2 microns as would be inaccordance with the following equation:

S(CTC)=0.8*R _(D)+2*R _(D)  Eqn 3

Although regular spacing of the plenirons 200 in the array 110 would bemore predictable and create a regular angular dependence of the powergenerated, randomly distributed devices would also function with similarcapability as long as the randomness in spacing averaged to nearly theabove mentioned values. In general, if the occluded area of thesubstrate exceeds more than about 12% of the surfaces of the plenirons200, then the performance may be degraded similarly. No more than about25% of the 90 degree incident area of the device should be planar floorarea. Similarly, off-angle at approximately 45 degrees the devices inthe array should not occlude more than about 20% of the nearest neighbordevices under worst-case circumstances, azimuthal variations. Althoughit is acknowledged that packing the plenirons 200 to such an extent thatocclusion is greater than about 50% will still provide benefit overplanar devices, especially off-angle, it would be expected that thearray 110 performance may be degraded by more than the sine of theincident angle squared times the occlusion ratio, at least.

Referring now to FIG. 10 , an example of the density of states for aplanar photovoltaic device will be discussed. In one or moreembodiments, one performance benefit of an array 110 of plenirons 200may be in peak power generated, as well as integrated power over allincident angles and diffuse light incidence. Because the optical volume,and TIR, characteristics of the array 110 or plenirons 200 allow farhigher power production at more oblique angles of incidence than planardevices, up to about 2× to about 2.5× the integrated area under theexponentially decaying attenuation curve of a planar array as shown inFIG. 10 over a full daytime can be achieved.

Referring now to FIG. 11 , the density of states for a plenironphotovoltaic device will be discussed. In a pleniron 200 the opticaldensity of states is increased in lateral directions by each individualpleniron in the array 110 focusing the light increasingly inward, byTotal Internal Reflection, as discussed above, and retaining the lightin a cavity resonator of the correct proportional dimensions. In thevertical direction, out of the substrate 212, the optical density ofstates is homogeneous and even. Although the pleniron 200 may beinhomogeneous in its construction, due to plenirons 200 being distinctfrom the spaces between them, the effective density of states, taken asan average over a large area of many plenirons 200 in the array 110, isa constant in the z-direction. The pleniron 200, due to Optical volumeeffects, will produce a step-function curve, proportional to the opticaldepth of the device, as shown in FIG. 11 .

To achieve this optically, the pleniron core 210, as a function ofmaterial set the absorber material, window layer, and TCO, may be sizedsuch that 99%, or about 3 Skin Depths, of optical absorption path lengthare traversed within one to five reflections across the interior of thecore material and/or the window layer. This depends on the materialset's absorption coefficient, or the complex part of the index ofrefraction, k. This varies by the dispersion relation with wavelength inthe material. Some examples of material sets that may be utilized inexample embodiments are shown in Table 1, below.

TABLE 1 Material Properties of Example Material Sets Eg (Band 99% n kGap Max Path Material Set (Index) (extinction) eV) Wavelength LengthPolysilicon 4.47 1.95E−02 1.1 1.13E−06 4.70E−06 Crystal Silicon 3.761.27E−01 1.1 1.13E−06 1.32E−04 Amorphous Si 4.96 2.19E−02 1.75 7.10E−075.20E−07 Gallium 3.42 1.91E−01 1.42 8.74E−07 3.25E−05 Arsenide Cadmium2.68 1.87E−02 1.44 8.62E−07 2.53E−06 Telluride CIGS 2.47 2.02E−02 1.498.33E−07 7.20E−07

In one or more embodiments pleniron 200 may comprise a meta-material.The extinction coefficient, as one example, of the silicon, and as oneof many possible embodiments, as the absorber 208 material, allows acertain path length for the light within it as in Table 1, above. Ifmeasured macroscopically, however, the extinction coefficient of thepleniron 200, for instance as measured in a Reflectometer orSpectrophotometer, will be nearly infinite. This is due to the lightabsorbing and retention properties possible due to geometry and totalinternal reflection.

In one or more embodiments, the layer doping profiles and the intrinsicmaterial properties may be tuned, or optimized, to maintain theappropriate widths of the depletion region between the N and Psemiconductor layers, weighted for a radial junction with an inversesquare concentration gradient. The depth of the depletion region, whichshould be designed to extend over at least 90% of the width of N and Pregions, is determined by the following parameters: The intrinsicsemiconductor number density in the Conduction and Valence bandsrespectively:

$\begin{matrix}{n_{C} = {{\exp\left( {- \frac{e*E_{gap}}{2k*T}} \right)}\left( {2\left( \frac{2\pi k*{m_{e}\left( m_{eff}^{e} \right)}*T}{(\hslash)^{2}} \right)^{3/2}} \right)}} & {{Eqn}4}\end{matrix}$ $\begin{matrix}{n_{v} = {{\exp\left( {- \frac{e*E_{gap}}{2k*T}} \right)}\left( {2\left( \frac{2\pi k*{m_{e}\left( m_{eff}^{h} \right)}*T}{(\hslash)^{2}} \right)^{3/2}} \right)}} & {{Eqn}5}\end{matrix}$

Here the difference in the two formulas is simply the difference in thelattice effective masses of holes and electrons for the valence andconduction bands respectively. This leads to the Built-In potentialacross the depletion region to be:

$\begin{matrix}{V_{bi} = {\frac{kT*{\log\left( \frac{n_{A}*n_{D}}{\left. {n_{c}*n_{v}} \right)} \right)}}{e} + E_{gap}}} & {{Eqn}6}\end{matrix}$

Here, the n_(A) and the n_(D) are the number concentrations in thedopant acceptor and donor bands. E_(g) is the band gap energy.

Note that the electric field across the depletion region, which may bemaximized to achieve high exciton acceleration and lower thermalizationlosses, is this V_(bi) divided by the width of the region. If thematerial properties significantly reduce charge screening such as, Debyeor Fermi-Thomas screening, naturally a thinner layer system will achievehigher electric fields. The resulting penetration of the depletionregion into the N material will be determined as follows:

$\begin{matrix}{W_{N} = \sqrt{\frac{2\epsilon*\epsilon_{0}*n_{A}*V_{bi}}{e*{n_{D}\left( {n_{A} + n_{D}} \right)}}}} & {{Eqn}7}\end{matrix}$

The penetration of the depletion region into the P material exhibits asimilar profile. The dopant concentration in a regular layer,non-radial, or planar thin film, would be proportional to the following:

$\begin{matrix}{{dC} = {{n\left( {{or}p} \right)}*{\exp\left( \frac{e*E_{A}}{kT} \right)}}} & {{Eqn}8}\end{matrix}$

Once the uncorrected dopant levels are determined from the above, toobtain the full depletion across the P and N layer regions, thefollowing weighting factor is used in the outer most layer, whether itbe a P or N semiconductor layer, to determine the final doping level.Note, as a rule, that the doping concentration would be denser in theunderlying layers, since the outer regions would be of greater totalvolume. One principle is that the total number of free charges, at aparticular operating temperature, may be approximately equivalent acrossthe DZ. The dopant correction factor for the radial junction is:

$\begin{matrix}\frac{\left( {d_{N} + R_{c}} \right)^{2} - R_{c}^{2}}{\left( {d_{int} + d_{N} + R_{c} + d_{P}} \right)^{2} - \left( {d_{int} + d_{N} + R_{c}} \right)^{2}} & {{Eqn}9}\end{matrix}$

Refer to FIG. 4 for reference of the layer thicknesses in Equation 9.Note here, as shown in cross-reference sections, that back contact 214is a high conductivity “mirror” layer used for pleniron cores 210 thatare semiconductor absorbers, semiconductor layer 216 and semiconductorlayer 222 are doped semiconductor regions, P or N respectively,intrinsic layer 224 is an intrinsic semiconductor region for chargedepletion, and TCO layer 218 is the transparent conductor. Note that inembodiments without an intrinsic region, which not provided for regularP-N junction systems, the d_(int) in Equation 9 is set to zero.

Referring now to FIG. 12 , a graph of voltage versus junction depth of apleniron in accordance with one or more embodiments will be discussed.The doping correction factor may be multiplied by the previous dopantconcentration calculation, that is in the doped semiconductor layer withthe greater total volume, outside layer, to ensure that the total freecharge number on each side of the metallurgical junction is equivalent.The potential profile of the resulting junction is similar to thefollowing, assuming that the active dopant density is equivalent acrossthe metallurgical junction as shown in FIG. 12 . The graph of FIG. 12above illustrates conditions of the use of poly-nano crystallinesilicon, with commensurate effective masses of 0.49 and 0.98 electronmass for electron and holes, respectively. In addition, the temperatureis standard room temperature of 300 Kelvins. The band gap is set at 1.1eV, the real part of the dielectric constant is 3.2 and the activedopant atom number density (per m{circumflex over ( )}3) is10{circumflex over ( )}22 in each region.

It should be noted that the voltage of FIG. 12 is larger than the bandgap of the material. This is a natural occurrence of the semiconductorequations above, where the band gap is the starting point of voltage,only first term, but also dependent on the logarithmic term which addsto the voltage if the numerator is larger than the denominator, forexample if the number of active dopant carriers, N_(a) and N_(d), islarger than the intrinsic number in the conduction and valence band orbands, respectively. This involves a high quality semiconductor materialwith a Debye, or Thomas-Fermi, screening length of greater thanapproximately 20% of a given layer thickness. In addition, as mentionedabove, the doping levels delineated are used in the layer thicknessesoutlined or quasi-neutral regions of the PN junction will act asresistances which decrease the open circuit voltage (V_(oc)). The dopinglevels also may not be so great that they either involve negligiblysmall thicknesses for full depletion, or they cause degenerate dopantband splitting into wide regions on the E_(c)/E_(v) energy diagram.

The situation of a nearly fully depleted region, lack of quasi neutralregions, high-quality material, and/or non-degeneracy causes there to bemassively dense charge clusters near the back and front contactmaterials. This is especially true at the back contact where theconductivity is higher and the radius is smaller than the front contact.The PN junction, if properly designed, as above, will naturally causeequilibrium of spatially separated like charges with high densities. Theregion between these two charge dense clouds will have charge densitiesup to about 10 to about 14 orders of magnitude less charge than theintrinsic material per m{circumflex over ( )}3.

Referring now to FIG. 13 , FIG. 14 , FIG. 15 , FIG. 16 and FIG. 17 ,graphs and illustrations of charge density in a pleniron in accordancewith one or more embodiments will be discussed. When the charge densityat the back contact 214 has been increased by the equilibrium design ofthe junction, the charge density, plotted on the previous potentialgraph, will appear similar that shown in FIG. 13 . This will allow alocally dense charge of fermions, electrons, at the back contact thatwill have a Full Width at Half Maximum (FWHM) of less than about 1% ofthe width of the spatial layer. In the case of the nano-crystallinesilicon, of high quality, this will be about 5-10 nm or less. Likewise,a similar concentration of the opposite charge carrier, in the presentcase within an N-type window layer, holes, forms either near theinterface or within the transparent conductor 218. In addition, as shownin FIG. 15 , the radial electron and hole densities (charge density)along the reference line in FIG. 14 , is as follows. In the class ofembodiments with semiconductor pleniron cores 210, the electrondistribution, commensurate with the optical density and that of holes,is illustrated similarly to FIG. 14 .

As shown in FIG. 16 , if the local density of the fermions, confined bythe built in electric field of the junction equilibrium and the backcontact Schottky effect, is greater than the Plasma frequency, definedbelow, then this charge cloud will act as an elastic mirror andresonator surface for photons. The electromagnetic radiation will notonly reflect from the electron distribution but the electrons willparticipate in resonation due to their interactions with each other,both Coulombic, and quantum mechanical exchange forces, and the incidentlight. The plasma frequency is:

$\omega_{p} = \sqrt{\frac{ne^{2}}{m_{e,h}^{*}\epsilon_{0}}}$

Where m_((e,h)) are the respective hole and electron effective masses,ε₀, is the permittivity of free space, and n is the concentration ofelectrons in the highest density region, number per unit volume. Theelectron distribution in a radially distributed junction, as describedabove will be non-planar, and be represented by the following:

${{eDist}\left( {r,\lambda_{0}} \right):} = \frac{r{\exp\left( {- \frac{r^{2}}{\lambda_{0}^{2}}} \right)}}{\lambda_{0}}$

Using a Debye screening length of an appropriate size for the material,determined by the following:

$\sqrt{\frac{10.6*e*\epsilon_{0}*n_{e}}{1.36}}$

The above expression gives the following graph shown in FIG. 17 of theelectron distribution, in a spherically symmetric ring around the radiusof the back contact, as a function of distance from the back contact.The vertical axis is the number of electrons per cm{circumflex over( )}3 as a function of distance from the back contact material. Clearlythe maximum is over 4*10{circumflex over ( )}15 electrons. Note thatthey are confined to a space of less than 100 angstroms. Given the smallvolume the total electron density exceeds 10{circumflex over( )}28/cm{circumflex over ( )}3. At this level the resonating electronscan elastically mirror and exacerbate light's interaction.

Typical known waveguides use high conductivity metallic surfaces orcoatings to decrease losses from skin-depth effects and decayingevanescent waves penetrating the metal surface at each reflection.However, even with high quality and conductive surfaces there ismeasurable loss at high frequencies, such as visible light, due to theelectric and magnetic field portions of the transverse and tangentialcomponents penetrating by 1/e distances of a few atomic monolayers. Thefully depleted region in the pleniron 200, which produces the highdensity charge cloud near the back contact of the device, has a peakcharge carrier density at least three orders of magnitude higher than ametal's Sommerfeld model free electron gas. This charge distribution,composed of electrons or holes, responds to the oscillatory fields ofthe electromagnetic radiation completely elastically and reflects thelight without loss. Therefore, the charge cloud will act as a waveguidesurface that eliminates skin depth loss and improves the performance ofthe device. Since the reduction of the evanescent wave reduces opticallosses, and removal of photons before exciton generation, the chargecloud reflection effect will appear on an I-V graph as an improvement indevice output current.

While all currently known photovoltaic devices are limited in efficiencyby exciton thermalization, the short electronic distance, presented as aresult of the fully depleted region, will reduce thermalized chargecarriers by as much as 90%. Thermalization, or the inelastic scatteringof excitons, electron, hole, or both, to produce phonon latticevibrations as heat due to collisions, is reduced from 10{circumflex over( )}−8 seconds to a range of 10{circumflex over ( )}−11 to 10{circumflexover ( )}−14 seconds due to two factors. First, the high electric fieldacross the depletion region, in addition to the short distance, causescharge carriers to be accelerated across the junction and into the backcontact Fermi-gas in a time far shorter than the minority carrierlifetime of the bulk semiconductor material. Whereas typical carrierlifetimes are on the order of 10{circumflex over ( )}−8 seconds, fornon-orientable materials like amorphous silicon, for example, shortfield regions of several microns can be accelerated to the respectivecontacts in a matter of as little as 10{circumflex over ( )}−11 to10{circumflex over ( )}−14 seconds. Second, the lack of quasi-neutralregions in the device, due to the full depletion, removes both chargedand neutral locations from acting as inelastic scattering centers ortraps. Drift and diffusion, or the pushing of charge carriers throughthe quasi-neutral regions due to screened Coulombic repulsion, is nolonger a factor in the pleniron 200. This will add to the overallcurrent output of the device due to increases in I-V curve fill factorfrom better Shunt Resistance. Devices with this feature will have ShuntResistances at least 25% better than corresponding planar thin filmdevices.

The conversion of photo-created excitons in the depletion region willadd to the overall current output from the device once the chargecarriers are collected in a metallic Fermi gas at the back or frontcontacts. This occurs as a result of the additional potential energy,from electrons elevated higher into the conduction band from deeper inthe valence band, converting into kinetic energy in acceleration towardsthe Fermi Gas. The added kinetic energy amounts to a perturbation to theFermi Distribution function, which is shown in and described withrespect to FIG. 18 , below.

Referring now to FIG. 18 , an example diagram of the energy band diagramfor crystalline silicon, an indirect band gap semiconductor, inaccordance with one or more embodiments will be discussed. As shown inFIG. 18 , the vertical axis is energy (E) and the horizontal axis is thek-vector, or crystalline phonon lattice momentum. Typical photovoltaicdevices, with drift diffusion regions allow photon-excitontransformation reactions from band edge to band edge as is shown by theshorter line marked as A. Although the photon energy may be in excess ofthe gap, the forbidden region, energy, the extra potential energy, maybe lost due to scattering and recombination in the drift/diffusionregions. The longer line marked as B is an example of the plethora ofmore energetic photons that can, in a pleniron 200 with tuned depletionregions, allow the added potential energy to be converted into useablepower as output.

Referring now to FIG. 19 , a graph of Fermi distribution for an examplepleniron in accordance with one or more embodiments will be discussed.As shown in FIG. 18 , the extra length in energy units of eV of thelonger line B over the shorter line A is the photon energy, oncetransformed into exciton kinetic energy that can be recovered asadditional power output by a photovoltaic device. The Fermi Distributionis:

$\begin{matrix}{{f(\varepsilon)} = \frac{1}{{\exp\left( \frac{\varepsilon - \varepsilon_{F}}{kT} \right)} + 1}} & \end{matrix}$

The electronic metallic density of states is:

${D(\varepsilon)} = \frac{\sqrt{\varepsilon}\left( {2m*\varepsilon*m_{eff}} \right)^{1.5}}{2\pi^{2}\hslash^{3}}$

The plotted Fermi distribution of FIG. 19 is for a Fermi energy of 2 eVand 300 K temperature where the vertical axis is the number of electronsin the state with the energy on the horizontal axis. Because they areFermions and obey the Pauli Exclusion Principle, states of +½ spin and−½ spin are regarded as different states.

Referring now to FIG. 20 , a graph of Fermi Equilibrium distributionwith hot electron perturbation in a pleniron in accordance with one ormore embodiments will be discussed. The perturbed Fermi distributionfunction looks like the graph of FIG. 20 when a Gaussian is added thatrepresents an injection of hot electrons. Here the center of theGaussian distribution of hot electrons is at approximately 3.5 eV with a1/e width of approximately 0.78 eV. This represents charge carrierexcitons, created by energetic photons, being absorbed into the Fermigas of the metal without losing their energy to inelastic scatteringcenters in the semiconductor material. The shape of the Gaussian occursas a result of a statistically random model of the location within thedepletion region where the photon is absorbed. The total number ofelectrons in the perturbed ensemble of electrons is as follows:

${N_{T}(\varepsilon)} = {\frac{\gamma\varepsilon^{1/2}e^{{- \mu}/{KT}}}{e^{{- \mu}/{KT}} + e^{\mu/{KT}}} + {\alpha e^{\frac{- {({\varepsilon - a})}^{2}}{b^{2}}}}}$

Where the first term is the usual number distribution, from the productof the Density of States and Fermi Distribution, and the second term,independent of temperature, is the perturbation.

Calculating the total Internal Energy of the perturbed free electron gasprovides the following:

${U_{Perturb}(T)} = {{- \frac{\sqrt{\pi}t^{3/2}{{PolyLog}_{\frac{3}{2}}\left( {- a} \right)}}{2a}} - \left\lbrack {\frac{\alpha}{2}\sqrt{\pi}\left( {{{erfi}\left( \frac{b}{a} \right)} + 1} \right)} \right.}$

Once again the first term comes from the typical Fermi number density,and the second from the perturbation. Once again, the perturbation termis independent of T.

Equating the unperturbed Internal Energy to the perturbed InternalEnergy allows us to calculate a new equilibrium electron gastemperature. The higher electron gas temperature immediately leads tohigher electron scattering rates and higher individual electronvelocities. The higher electron velocities translate directly to higherdrift velocity of the electron gas which, under the influence of fields,leads to more current. Referring to the terms as the following:

${\alpha = \frac{\sqrt{\pi}{{PolyLog}_{\frac{3}{2}}\left( {- a} \right)}}{2a}}{{{And}\beta} = {\frac{\alpha}{2}\sqrt{\pi}\left( {{{erfi}\left( \frac{b}{a} \right)} + 1} \right)}}$

The change in electron temperature is as follows:

${\Delta T} = {\frac{1}{k_{b}}\left( \frac{\beta}{\alpha} \right)^{2/3}}$

Therefore, the temperature increase is proportional to the ⅔ power ofthe ratio of the energy contribution of the perturbation to that of theequilibrium electron gas. Since in the non-relativistic regime of thecarrier velocities they are proportional to the square root of thetemperature, the velocity distribution varies as follows:

${v(T)} = {\sqrt{\frac{3}{m_{e}}}\left( \frac{\beta}{\alpha} \right)^{1/3}}$

Current increases would be proportional to the increase in velocity,cubed, due to the orthogonality of the three coordinate directions:

${J(T)} \propto {\left( \frac{3}{m_{e}} \right)^{3/2}\left( \frac{\beta}{\alpha} \right)}$

In one or more embodiments, the design of an array 110 of plenirons 200may be considered. Optimization of array 110 is begun with a materialsystem selection, the decision for which is based on processcomplication, cost, screening/recombination length electronic band gapwidth performance, and/or optical path length. The performance basedfactors are discussed briefly, below.

Electronic band gap width may be a factor. Photons with energy less thanthe band gap energy of the material they are incident upon are absorbedas heat instead of as excitons that can add to power production. Forthis reason, selection off a material with a smaller band gap(crystalline silicon has 1.1 eV as opposed to amorphous Si with 1.75 eV)is preferable so that light in the red to infrared parts of the solarspectrum can be captured. This factor is balanced and weighed againstsome of the other factors, below.

Screening and recombination length of a semiconductor is a factor toconsider since this will not only limit the device open circuit voltageV_(oc) but also will affect output current. The carrier lifetime is alsorelated to this factor. If the lifetime of a carrier (portion of acreated exciton) is less than the average time for the carrier to getout of the semiconductor material in the device, then the carrier willlikely be absorbed by inelastic collisions in the material andrecombined (electrons with holes and vica versa). The probability thiswill occur is greater in materials that are disordered, such aspolycrystalline, with random grain boundary orientations, and amorphousmaterials, which have no regular structure.

Direct and Indirect Band Gap materials are another factor. The energyband diagram of a semiconductor material is a flattened out version ofthe surface of the First Brillioun Zone in lattice phase space (momentumand energy space). Conduction band minima and valence bands' maxima maynot necessary coincide in the same region of momentum space, the kdirection. This means that raising the energy of an electron itself isnot sufficient in an indirect bandgap semiconductor since the v-bandmaxima is not directly below the conduction band minima. A momentum, orlattice phonon transition is also necessary. The probability of this isless than in a direct bandgap semiconductor, so optical path lengths incrystalline silicon is much longer than in direct band gap materials.

Cost and process considerations also may be factors. Although amorphoussilicon has a very short carrier lifetime, causes recombination readily,and has a short band gap, it is very inexpensive to produce and can bedeposited by equipment in vacuum in short time frames for highthroughput. It can also be deposited at relatively low temperatures sothat it does not affect the integrity of other materials (prior to thea-Si or subsequent) or their interfaces, such as thermal delamination.Prior to the pleniron 200 device, crystalline silicon has been known tohave a very wide band gap, low carrier recombination rate, be highlyordered, requires high temperatures to produce, and has a long opticalpath length. As noted above, however, in a 3D device a long optical pathlength becomes a positive since less material is used reducing cost. Themeta-material-based pleniron 200 device works as if it is thicker thanit actually is.

Material Selection may determine other factors. Once the material systemselection has been made, on the basis of performance and cost, and thebulk properties of the absorber material is known, the sizes of thelayers are determined on the basis of previously discussed rationale.

The pleniron core 210 is made to such a size that about 90% to about 99%absorption probability occurs within three passes across an averagediameter. If the pleniron 200 is made such that the core is conducting,as in another embodiment illustrated later, and the absorber layer is aconformal pseudo-spherical layer over the conductor, then the layerthickness of that material also determined according to the argument ofthe ArcSin[ ] function in Equation 1 discussed, above. Since this ratio,the argument, produces the minimum angle at which light from air willexperience total internal reflection inside the underlying absorbermaterial, a reasonable selection of the ratio is made. If a selection ofabout 0.5, for instance, is made, then any compound angle of incidence,meaning the multiplication of the direction cosines of both theta, theangle relative to the normal of the substrate, and phi, the angle aroundan individually considered pseudo sphere, greater than 30 degrees willbe totally internally reflected inside the absorber material and trappedcompletely. The remaining π/6 subtended solid angle more normal to theangle of incidence in θ is refracted into the absorber 208 and keptthere in accordance with its polarization's reflection probability. Thisis shown below for a material, such as Indium Tin Oxide, as an example,as the transparent conductor, with light incident from air.

Referring now to FIG. 21 , graphs of transmission probability by angleof incidence for Sigma and Pi polarizations, respectively, for apleniron in accordance with one or more embodiments will be discussed.From the graphs shown in FIG. 21 , the Pi polarization may be preferableat higher, more glancing angles. Since white light is a linearcombination of both the Pi and the Sigma polarizations it isadvantageous that the pleniron maximizes absorption for near normalincidence in the sigma polarization, but takes full advantage of thenearly total absorption of the Pi polarization at off-angle or aroundthe sides of the pseudo sphere of the device. Since polarization isdetermined by the plane of incidence of the light, which changescontinually around the sidewalls of a pseudo sphere of a pleniron 200,the Sigma is accentuated at near normal incidence, and the Pipolarization is accentuated for all other more glancing angles.

Provided with the argument for the ArcSin function for Equation 1, andan estimate of the required minimum angle for TIR in the core orunderlying absorber film, Equation 1 may be utilized to calculate thethickness of absorber 208. The rule delineated, above, that is of theouter TCO being approximately about 1 to about 0.67×the thickness of theabsorber 208, is then used to approximate the thickness requirement ofthe outer transparent conductor. Although material considerations shouldbe taken into account, such as material resistivity and the seriesresistance, an appropriate balance may be achieved with opticalmaterials that remain conductive in the layer thickness required for thedevice's optical properties to function.

With the thickness of TCO 218 determined, and the absorber 208 thicknessapproximated, Equation 1 may be used to determine the diameter ofpleniron core 210 to achieve the desired TIR in the materials. However,the material system must now be taken into account again, for electronicreasons, and process reasons, such that other parameters discussed,above, are fulfilled. This means that, for the pleniron 200 to functionoptimally, a fully depleted layer may be developed. Equation 7 is thenused to determine the dopant concentration of the N (or P) layernecessary to fully deplete the opposing layer beneath it. Equation 9 isthen used to calculate the resulting dopant in the other layer (P or Nas opposite to above), that is above the other layer (e.g. the outerlayer is the so-called Window Layer). Note, again, that Equation 9 isthe so-called dopant weighting formula, and accounts for the largervolume of material at a larger radius in a pseudo sphere PN or PINjunction to maintain charge balance.

If the above dopant levels are within the acceptable range of impuritiesin the material system, as to not increase recombination or create asemi- or fully-degenerate semiconductor device, then the proper balancehas been achieved and electronic considerations have been developed.Typical values for amorphous silicon are 10{circumflex over( )}17/cm{circumflex over ( )}3 for N type dopant and 3*10{circumflexover ( )}17/cm{circumflex over ( )}3 for the P type dopant material.Note, however, that the weight formula, Equation 9 will modify thissignificantly if the layers have larger radii, and the relation of the Player to the N layer (above or below). Crystalline silicon will abide bythe same weighting rules, but dopant activation in that material is fareasier and lighter doping is necessary. Typical values are 10{circumflexover ( )}14 for N and 5*10{circumflex over ( )}15 for P.

pleniron 200 spacing consideration and optimization are additionalfactors. The spacing of the plenirons 200 in the array 100 allowsoptimum lighting of the devices from or nearly all angles of incidencewith minimal shadowing. Although a regular structure is necessary forthis optimization, the device can be similarly irregular, and stillfunction, albeit to a lower performance level.

Once the sizes of the layers and the underlying pleniron core 210 areknown, addition may be used to determine the size of the overallpleniron 200. Then the following formulas can be used to determine theoptimum spacing to achieve the best sidewall exposure of the plenirondevices at all orientations in θ and φ.

Using Equation 1, or the argument of the ArcSin function in Equation 1,and choosing an appropriate ratio for that argument, less than aboutone, such that the incident angle from air (or vacuum) into thetransparent conductor is totally internally reflected in the absorber,an absorber thickness appropriate for the material system selected fromabove may be solved.

As a general rule the Transparent conductor, whether an oxide of ametal, or doped oxide, or selenide, or otherwise, must be of a thicknessbetween about 0.67 and one times the thickness of the underlyingabsorber 208. Since the transparent oxide is generally a lower index ofrefraction than the absorber material (which allows for stepped indicesas the radius decreases inward) the thickness rule is applied to preventgrazing incidence and subsequent exit into the transparent conductor andthen immediately out. Although this scenario may lead to a subsequentabsorption, some percentage, perhaps as high as 25%, of the light fieldstrength is lost through a pass through the Transparent conductor fullpath. An alternative scenario is the acceptance into the transparentconductor followed by internal reflection, albeit imperfect or rejectedacceptance into the absorber. This scenario causes a significant amountof trapped photons to be absorbed as heat only in the transparentconductor, if it is too thick proportionally.

Calling the argument to the Arcsin function in Equation 1, g, we solvefor absorber thickness using 0.75*d(abs) as a substitution for thethickness of the transparent conductor in the equation for g. We obtainthe following for the absorber thickness that will meet the requirementfor the incident angle TIR in absorber 208.

d _(Abs)=(n ₂ −g)R _(c)/(1.75*g)

Note that here n2 is the index of refraction of the transparentabsorber, as in Equation 1, g is the argument of the Arcsin function,R_(c) is the radius of the underlying pleniron core 210, and the result,d_(Abs) is the optimum thickness of the absorber material, including P,N, and Intrinsic semiconductor regions, as needed. Note that theparameters for the electrical junction of the device dependent on thematerial system selected are discussed herein. Therefore, the materialsystem, complete with dopant activation and carrier characteristics,should support the thickness of absorber selected by the above analysis.The absorber 208 thickness should be sufficient to allow wavepropagation and standing wave development within its layers toparticipate in optical volume and uniform density of photon statesphenomena.

The optical volume effect, that is the homogeneity of photon density ofstates throughout the entire optical thickness of the device to whateverdepth is desired and allowed by the material system, depends on wavepropagation, standing wave development, and a steady state density ofstates in the absorber material. Therefore, the absorber materialthickness should not be sized minimally such that its physical thicknessis less than allowable half wavelength of light which is intended to beabsorbed. This is referred to in waveguide and electromagnetic designdisciplines as the Cutoff Wavelength where the minimum thickness of thepropagatable material is less than a half wavelength of the lightincident. Since the wavelength of interest is dependent on the band gapof the material, it may be in the ultraviolet (UV) region as theminimum, so wavelengths may be less than 300 nm. For absorber indices ofrefraction of 3, for instance, this requires that the absorber thicknessbe greater than about 50 nm, at the very least. Note that, aside frommaterial savings, there is not significant harm in having more radialmodes of propagation, as well as circumferential, than the fundamental,half wavelength. Therefore, having absorber thickness significantlygreater than cutoff, such that they meet the ratio supplied by Equation1, for g, will allow for optical efficacy and enhance, not degradeenergy conversion efficiency.

Restricting the photon propagation modes, however, by operating near thecutoff wavelength, may severely limit efficiency due to the requirementthat solar plane waves conform to spherical, or pseudo spherical, modesin propagation in the absorber material. This transform mathematically,from d'Alembertian plane wave propagation to spherical Hankel functions,spherical harmonics, and Legendre Polynomials, restricts the number ofallowable photon modes such that at least about 63% of the wavelengthsof visible light are not allowed in.

The worst case scenario, that is operating below the cutoff wavelength,allows only evanescent waves within the absorber 208. Although thesub-wavelength propagation concept is of interesting research in opticalwaveguides, it is of little use in photovoltaics. Evanescent waves carryno energy and cannot convert their effectively zero power Poyntingvector into any excitons. Any presumed superposition of evanescent wavesin myriad sub-wavelength structures have not been shown to produce anypower of any meaningful value. This brackets the size of the absorber208 layer, considering the minimum, or the cutoff wavelength value, andthe maximum, being that driven by the g value, and design tempered byelectronic selection considering screening length and ultimate V_(oc)production. Recall that the requirement that the P-N or PIN structuremust be fully depleted for this to function completely according todesign parameters.

Spacing of the pleniron 200 elements in a regular array, or the averagespacing, if controlled, in an irregular array, can be optimized suchthat the plenirons 200 are not obstructing or shadowing each other overthe widest possible range of incident angles. This will allow anuntracked solar array 110 of plenirons, in a plenistell module, toproduce the maximum amount of power when angles are not normallyincident. Because the optical volume, and TIR, characteristics of thearray 110 allow far higher power production at more oblique angles ofincidence than planar devices, up to about 2× to about 2.5× integratedpower over a full daytime can be achieved. The meta-material plenistellarray will not obey the sinusoidal Cos[θ] decrease from normal incidencelike a planar array. Although the array 110 still would make the maximumamount of power from normal incidence, thereby maximizing the potentialfrom the largest subtended area, its power production capability will bea much less subtended-area-related function of angle.

Since, depending on the level of embedding of the pleniron core 210 inan underlying substrate, the radius of the finished pleniron 200 issimilar to its height, calculations of the optimum spacing can determinethe shadowing efficacy of the finished radius as well. If the plenirons200 are arranged in a regular lattice-type structure in two dimensionson an underlying substrate, their arrangement is determined by aso-called basis set. The basis set has two fundamental parameters thatdetermine the location of the centers of each of the plenirons 200across the entire array 110. A simple example would be a rectangulararray, and a slightly more complex example would be a hexagonal ortrigonal array.

Using Wolfram Research Mathematica notation as a mathematical method forreporting analysis, the following is an example of a very generalizedmathematical basis set for any two dimensional array of objects:

a1V[a_,b_,c1x,c1y_]:={a*c1x,b*c1y};

a2V[a_,b_,c2x,c2y_]:={a*c2x,b*c2y};

Here a and b are constants and the c1x, c2x, c1y, c2y are the vectorcomponents of the basis unit vectors that describe the directions, to bemultiplied by the a or b constants, to obtain the regularized spacing.

The following is then utilized to create a regular array in a virtualmathematical environment for visualization and analysis of lightobstruction on the devices:

basisSetSphere[xM_,yM_,a1_,b1_,c1x1_,c1y1_,c2x1_,c2y1_,h1_]:=Flatten[Table[{Append[x*a1V[a1,b1,c1x1,c1y1]+y*a2V[a1,b1,c2x1,c2y1],{x,−xM,xM},{y,−yM,yM}],1]

Note that in this example the h1 variable is the same as the radius ofthe average pleniron device and the xM, yM are merely the maximum sizeof the display of the device array. The Mathematica code necessary tomanipulate the finished array is as follows:

sphBasisManipulate1=Manipulate[sphBasisArray[10,10,q,q,1,0,0.5,0.866025,h,r,x,y,z],{{q,6,“Spacing(CTC)”},4,20,Appearance→“Labeled”},{{h,10,“PlenRad”},4,20,Appearance→“Labeled”},{{r,2,“PlenRad”},1,5,Appearance→“Labeled”},{{x,Pi/4,“x−Angle”},−Pi/2,Pi/2,Appearance→“Labeled”},{{y,Pi/4,“y−Angle”},−Pi/2,Pi/2,Appearance→“Labeled”},{{z,Pi/2,“z−Angle”},0,2Pi,Appearance→“Labeled”},FrameLabel→“PlenParameterManipulator”,ControlPlacement→{Top,Top,Top,Bottom,Bottom,Bottom}]

This results in the array 110 as shown in FIG. 22 from the definedcoordinates. The spacing, size, and orientation of the plenirons 200 arefactors to maximize the off-angle performance of the device over anentire daytime. As an example the array 110 of FIG. 23 is taken at anextreme angle, as would be viewable from the sun's viewpoint at anextreme evening or early morning position. Note that, at this extremeangle all of the plenirons may be obstructing each other, although notas much degradation would be apparent as with a planar array. One shouldalso note that the rotational angle, φ, from nearest neighbor to nearestneighbor vector, causes the most obstruction. The array 110 of FIG. 24is an example of the same extreme angle but with the φ rotated, in thistrigonal example, by π/6 radians.

To prevent the obstruction of the plenirons 200, allow the maximumOptical Volume to be evident, and allow the transmission curves of FIG.21 to be optimized, the outer edges of the plenirons 200 may be occludedby only that amount, about 0.8 to about 0.9, that is expected tosignificantly reflect and not absorb. This factor, the occlusion,referred to here as γ, can be a double check on the radius of thecompleted pleniron 200, and thus its height, in the following way. Oncethe device diameter is known from the calculations above from Equation1, the exposure ratio, γ, is used to determine the optimum pitch, orcenter to center spacing of the devices. This gives, as the pitch, a,the following:

α=(1+γ)D _(d)

where D_(d) is the finished pleniron 200 device diameter. This can thenbe used in conjunction with the prior calculations for the devicediameter to allow total internal reflection to determine all of theother parameters for the optimum pleniron 200, and their subsequentspacing into arrays 110.

If the pleniron's 200 basis set is such that it is a trigonal approach,for example, the following would be an example of how the distancebetween second neighbors, those opposed across basis vectors in a longorientation, would be calculated:

α_(L)=2 √{square root over (3)}(1+γ)R _(L)[1+(n ₂ −g)R _(c)]

Note that n2 is the index of refraction of transparent conductor, g isthe ration defined by the argument of Equation 1, and R_(c) is theradius of the inner core 210 of the pleniron 200.

If the plenistell 200 is untracked, relative to planar, not only willthe instantaneous power be nearly about two, or more times that ofplanar, but the integrated power over a daytime will be about 2× toabout 2.5×. However, if it is tracked, in an equatorial fashion, theinstantaneous power generated can be integrated over the daytime,modulated by the solar spectrum power reduction at extreme angles due toatmospheric scattering, e.g., Air Mass 1.5 standard from the NationalRenewable Energy Laboratory (NREL).

Power output can be maximized through the use of algorithms thatmaximize the exposure relative to the sun as a point source, minimizepleniron 200 shadowing and attempt to expose the largest possiblesurface area of the array 110 in the long orientation, as opposed to theshort. Note that this is illustrated in FIG. 22 through FIG. 24 .

Using trigonometric analysis for the angles of occlusion of theplenirons 200, the following transcendental equation is developed thatrelates the azimuthal angle of incidence (Phi−x in this example), andthe altitude angle of incidence, Theta−y in this example, to the angleof exposure, gamma. The equation to be solved is the following, forpartial hemispheres obstructing each other with changes in incident Phiand Theta:

$\begin{matrix}{\gamma = {{Solve}\left\lbrack {\frac{{atan}(y)}{r} - {{\cos(x)}{\tan(y)}} + {\sin(x)}} \right\rbrack}} & \end{matrix}$

The relevant solutions to the equation are as follows, performed usingWolfram Research Mathematica:

$\left. x\rightarrow{- {\cos^{- 1}\left( \frac{\begin{matrix}{{{- 2}\sqrt{{a^{2}r^{2}{\sin^{2}(y)}{\cos^{2}(y)}} + {2{ar}^{3}{\sin(y)}{\cos^{3}(y)}} + {r^{4}{\sin^{2}(y)}{\cos^{2}(y)}}}} -} \\{{{ar}\cos\left( {2y} \right)} + {ar} + {r^{2}\left( {{- \sin}\left( {2y} \right)} \right)}}\end{matrix}}{2r^{2}} \right)}} \right.$

In addition, the following solution is relevant as well, although for aseparate section of the Phi angle:

$\left. x\rightarrow{\cos^{- 1}\left( \frac{\begin{matrix}{{{- 2}\sqrt{{a^{2}r^{2}{\sin^{2}(y)}{\cos^{2}(y)}} + {2{ar}^{3}{\sin(y)}{\cos^{3}(y)}} + {r^{4}{\sin^{2}(y)}{\cos^{2}(y)}}}} -} \\{{{ar}\cos\left( {2y} \right)} + {ar} + {r^{2}\left( {{- \sin}\left( {2y} \right)} \right)}}\end{matrix}}{2r^{2}} \right)} \right.$

These solutions as shown in FIG. 24 relate the Phi to the Theta andproduce a surface of energy production with the vertical axis beingwatts and the two horizontal axes being the theta and the Phirespectively. Note that the x-axis, which ranges from 0 to Pi radians(3.14) represents the moving of the Phi angle, at a fixed Theta, over180 degrees of orientation. This is equivalent to moving the device inPhi from the long to short to long orientations 3 times respectively.

One example of the manufacture and process of this array 110 ofplenirons 200 is using Polycrystalline silicon deposition on top of apleniron core 210 of monocrystalline silicon. Adhering to the parametersof the ratio of Equation 1 and the subsequent parameters delineatedherein, the polycrystalline layer will be of a certain requiredthickness, sufficient to fully deplete the pleniron core 210, and bedepleted itself, such that electron and hole distributions are distinct.This is accomplished with Physical Vapor Deposition (PVD), whether RFamplified, biased, or otherwise, or via Chemical Vapor Deposition (CVD),using usual methods such as sub-epitaxial processes with organicprecursors or inorganics (e.g., Silane, trichlorosilane, dichlorosilane,disilane, TEOS, etc.).

The pleniron cores 210 may be embedded into an underlying substrate 212using a technique where they are created in a pseudo-spherical fashionprior to their utilization, embedded into a polymeric material to thedesired depth, followed by electrodeposition or sputtering of metal overthe exposed surfaces. If the pleniron core 210 is embedded to somewhatless than ½ of its diameter in the polymer material, the metallicdeposition will cover greater than ½ of the surface area of the exposedsurfaces. This is then regarded as the back contact material 214, thateither exhibits ohmic contact with the semiconductor pleniron core 210or a positively facing (current from semiconductor to metal)advantageous Schottky junction that will act as a heterojunction incombination with the PN or PIN junction of the device.

Another embodiment of the pleniron 200 based array that will alsoexhibit optical volume properties to the extent allowable by thematerial system may comprise a conductive pleniron 200, for exampleusing a polysilicon, metallic, an so on, pseudo-spherical pleniron core210 that would then have PN, PIN or Schottky diode type chargedisplacement properties. This films of the P, I (if needed) and Nmaterials would then be deposited over the micro- or nano-structuredback contact substrate. Of course, the substrate would consist of eitherconductor-based pleniron cores 210, embedded in metallic materials, or adegenerate semiconductor material, or an insulator (of polymer orinorganic type) that is structured and then metalized by an appropriatemethod, electroless metal, electrodeposition, or conformalPVD/Sputtering methodologies.

In the cases above, either with a semiconductor pleniron core 210, orwith a degenerate or conductor-based pleniron core 210 underlying thedevice, the layers of absorber could be deposited over themetallization, whether in PN, NP or PIN/NIP configuration, usingdepending on the material system, Chemical Vapor Deposition (CVD),Plamsa-Enhanced Chemical Vapor Deposition (PECVD), Physical VaporDeposition (PVD) which includes sputtering techniques, and/or AtomicLayer Deposition (ALD). In addition, it is considered viable to depositnano-grained N or P type semiconductor materials, of any variety, usingElectrophoretic Deposition, EPD. Various methodologies have differingadvantages with regard to cost, throughput, surface roughness, bulkmaterial quality, and/or contamination risk.

In each case, whether the material system is crystalline,polycrystalline, nano-crystalline, or amorphous, the layers are doped,or seeded with charge carriers, by adding appropriate small quantitiesof donor or acceptor materials, tuned for the material systemelectronically, to the layers, during deposition, whether for P or Ntypes. Intrinsic regions, if needed, may be left undoped or just lightlydoped. The appropriate doping levels are dependent on the materialsystem, as discussed herein, and selected to be optimum to fully depletethe various radially displaced layers of their charge carriers in anequilibrium state, no bias. Note that, as discussed herein, the dopingshould be weighted, or adjusted, due to the radial nature of thejunction. This is because there is greater volume in the outer lyingregions, due to the pseudo-spherical shape, and that greater volumeneeds fewer charge carriers, doping, per unit volume to obtain the sametotal number of carriers to support the junction depletion.

Noting the doping levels of the P and N regions respectively, in thecurrent example of silicon, either Arsenic (Ar), Phosphorus (P), orAntimony (Sb), for the N regions, and Boron (B) for the P regions. Whilethere are other N and P dopants, they are not typically as effective intheir doping capability due to higher activation energies, EA, orcrystalline defect producing effects in crystalline orpoly/nano-crystalline materials. If the material selection ismonocrystalline for the pleniron 200 then the wide array of selection ofdopants and the ease of production incentivize the selection of siliconas the base material. Naturally a PN junction is created through theapplication of epitaxial or ALD applied P and N silicon. High qualitynano-crystalline material can be used in a PN junction if theinteraction at the metallurgical junction is diffusion-limited and theinterface does not exceed about 50 Angstroms. Any increase in thediffusion across the metallurgical junction of the P and N junctionswill cause depreciation of the electrical properties of the device suchas V_(oc) and shunt resistance R_(Shunt), and may severely limitperformance exponentially with diffusion distance.

The upper levels of the pleniron 200 are to be made up of a transparentconducting material as the so-called top contact. This contact is thewindow layer, which allows light to complete the optical volume effectusing the ratio from Equation 1, allows it to enter the pleniron 200,and allows a conductive material with which to carry current in the formof electrons or holes, depending on the direction of the junctioncreated. This material can take the form of any conducting material thatis reasonably transparent, such that its absorption coefficient,typically, α, that comes out of the extinction coefficient, k, from thecomplex portion of the dielectric constant, ϵ. Examples of this aredoped Zinc Oxide, ZnO, with Aluminum (Al), or Boron (B), or a variety ofother conductive dopants. The mix of amorphous and crystallinematerials, with dopant, can be applied with Physical Vapor Deposition(PVD), whether radio-frequency (RF) biased or direct current (dc), or byChemical Vapor Deposition (CVD), or with Atomic Layer Deposition (ALD).The smoothest layers for the roughness parameters may be achievable withthe more conformal methods, especially ALD.

Other materials for use as a conductive transparent material may includeIndium Tin Oxide, ITO, doped Tin Oxide, B:SnO2, doped Nitrides, dopedsilicon oxy-nitrides. However, it should be noted that engineeringdesign criteria is such that, although only one pass of light throughthe transparent conductor 218 is involved, some materials, such as ITO,although highly conductive, are not especially transmissive oversignificant distances. As noted in earlier sections involving thegeometry of the devices ITO would be conducive to pleniron cores 210 ofsmaller diameter, such as might be used with materials with higherextinction coefficients than silicon, whether crystalline or otherwise.

Encapsulation as the final possible step in the production of an array110 may involve the use of a polymer material. This polymer material canbe any transparent, limited absorption coefficient material, such asethylene vinyl acetate (EVA), or polyimides or otherwise. In addition,encapsulation might occur automatically as a result of a superstraterather than a substrate construction, where a transparent material isstructured first and the subsequent layers, including semiconductorjunctions and transparent conductors, are added in the orderappropriate. This makes implicit that the pleniron structures will besurrounded by a material more optically dense than air. Although thedevice will perform differently as a function of the angle of incidence,there will be less dependence on the geometry. The dependence of thegeometry will be in accordance with, again, the parameters of Equation 1in the beginning of this document.

Other embodiments of semiconductor absorber 208 materials might beGallium arsenide, GaAs, Cadmium Telluride, CdTe, Gallium Nitride, GaN,CIGS, Cadmium Indium Gallium Selenide, or other binary or tertiarysemiconductor combination. Amorphous materials may include amorphoussilicon or lead or bismuth compounds or combinations thereof. Thesemight involve either a PN junction or a PIN junction depending on theabove.

The creation of the pleniron core 210 may be performed by perforatingsubstrates 212, micronizing them, and polishing themelectro-hydrodynamically to achieve the desired shapes while retainingthe necessary bulk material properties. It should be noted, however,that the scope of the claimed subject matter is not limited in thisrespect.

Although the claimed subject matter has been described with a certaindegree of particularity, it should be recognized that elements thereofmay be altered by persons skilled in the art without departing from thespirit and/or scope of claimed subject matter. It is believed that thesubject matter pertaining a photovoltaic device and/or many of itsattendant utilities will be understood by the forgoing description, andit will be apparent that various changes may be made in the form,construction and/or arrangement of the components thereof withoutdeparting from the scope and/or spirit of the claimed subject matter orwithout sacrificing all of its material advantages, the form hereinbefore described being merely an explanatory embodiment thereof, and/orfurther without providing substantial change thereto. It is theintention of the claims to encompass and/or include such changes.

In another embodiment, the plenistell, and even an individual pleniron,can act as any of a broad range of types of optical sensor because eachis a photovoltaic device in and of itself. Utilizing the plenistell inthis fashion in some examples involves a number of plenirons in an arrayas deemed necessary by a manufacturer or end-user. A photovoltaic deviceis defined as one that generates electrical current from an appliedvoltage and excitation by light. Therefore, the plenistell, set ofplenirons, or even a single pleniron, can be utilized, for example whencalibrated, to determine or sense a number of photons, or othervariables of impingent light, given the appropriate remaining unknowns.The number of photons, for example, can be determined from a measuredelectrical current generated, given illumination by a small spectralbandwidth source such as a laser.

Provided the layout of an array of plenirons in a given plenistell, asprovided in the above discourse regarding basis sets as discussedherein, a plenistell can determine the angle of incidence within a rangeof angles of periodicity. Because of the regular spacing of an array ofplenirons in this embodiment, a given pleniron can occlude the lightincident on one of its nearest neighbor and followed by a second-orderneighbor differentially as the incident azimuthal and altitudinal angleis changed. As further example, a rectangular array of plenirons in aplenistell, of design-intended extent, can produce a unique current orpower signature over a 90 degree azimuthal range and an approximately60-70 degree altitudinal range. Note that this effect can be present anddetectable with white light of a fixed radiance. Note that this wasdiscussed above and as shown in FIG. 24 .

Referring to the aspect of the discussion herein, where prior materialled to design criteria for the regular spacing of plenirons in aplenistell array, portions of the derivation of the following matter inthat discourse are provided herein as examples of algorithmicdevelopment to extract plenistell optical information. For example, asfurther introduced above, the design criteria for spacing of a regulararray come from optical, electronic, and other fundamental materialconsiderations. To prevent over “shadowing” of plenirons in an arraythat has been too packed, or not having them close enough together toavoid “floor” (or substrate) or glancing-angle pleniron reflections ineither Sigma or Pi types of polarization, optimal signal productionalgorithms, for the widest possible input angle range as possible, havebeen developed as described herein. To this end, to lead to equationsshown herein which then form the transcendental equation below:

$\begin{matrix}{\gamma = {{Solve}\left\lbrack {\frac{{atan}(\phi)}{r} - {{\cos(\phi)}{\tan(\phi)}} + {\sin(\theta)}} \right\rbrack}} & {{Eqn}.{Cl}}\end{matrix}$

These equations subsequently lead to the solutions shown in that samesection above. It should be stressed in reminder that γ is a complicatedsection of solid angle that is a function of angles θ and ϕ, transferredby symmetry to the center of a given pleniron, to provide the area of aneighbor pleniron not shadowed by the first and thus illuminated bylight incident from all θ's and ϕ's included. The equation providedherein, which includes pleniron information such as core radius andindices of refraction, was obtained by including Transmissioncoefficients, the probability of transmitting into the pleniron asopposed to reflecting off as a function of angle, for both the Sigma andPi polarizations of light. That equation is re-presented below:

α_(L)=2 √{square root over (3)}(1+γ_(max))R _(L)[1+(n ₂ −g)R _(c)]  Eqn.C2

Here, γ_(max) is clarified to mean an integration of γ over θ and ϕ.Note, also, that this equation includes geometrical considerations ofthe plenirons such as core radius and indices of refraction.Optimizations of these factors can, again, be provided by elaboration ofEqn. 1 herein.

In addition, geometrical and differential analysis of shadowing angles,as is shown in FIG. 26 for the angle ϕ, and in FIG. 27 for the angles θand ϕ, has provided, for hemispherical plenirons, the followingrepresentation of the angle θ as a function of ϕ, θ(ϕ):

$\begin{matrix}{{\theta(\phi)} = {\cos^{- 1}\left\lbrack \frac{\left( {a - {r_{0}\sin\phi}} \right)}{\left. {\sqrt{\left( r_{0}^{2} \right.} + \left( {a - {r_{0}\sin\phi}} \right)^{2}} \right)\cos\phi} \right\rbrack}} & {{Eqn}.{C3}}\end{matrix}$

Note that in FIG. 26 the constant r₀′ represents the radius of the baseof a repeated pleniron as this figure is a top view (from +z looking in−z direction). Here, the constant a is the center-to-center plenironspacing specifically in the “short” neighbor direction. The constant αrepresents the “long neighbor” center-to-center distance represented asα_(L) in Eqn. C2. FIG. 28A clarifies the nearest neighbor distance, a,in the same top view, and also shows a for a hexagonal pleniron arraytype. It also, notably, shows the coordinate formalism for the angle ϕ(absolute coordinates—where a selected pleniron center point is chosenas the origin and the unit cell is repeated in accordance with thelattice vectors discussed herein). FIG. 28B shows the same in anisometric view for clarity, although it includes the plenirons aswireframes of their outer shell. The height, h, of the pleniron is shownhere as well. FIG. 29A and FIG. 29B show the same, respectively, for arectangular pleniron lattice arrangement.

FIG. 27 brings special note in that it shows, as in FIG. 26 from a topview, the angle ϕ shifted by symmetry for clarity to a position off theedge of a “shadowing” pleniron onto the subject. Recall that ϕ is theangle (azimuthal from 0 to 2 Pi radians) from a line drawn through thecenters of the bases of a nearest neighbor, a, plenirons. At ϕ=0, forexample, at θ=0 (in plane of substrate view) all the plenirons would becompletely shadowed by the ones in front of them. Any slight angle,even, off of ϕ=0 would allow some incident light illumination of theplenirons behind. Including θ, as shown in the figure, which is afunction here of ϕ, provides a compound angle onto the subject pleniron.The vector r, from the center of the subject pleniron, shows the shadowline demarcation of the base edge of the shadowing pleniron as θ and ϕchange progressively. As the line shown is that progression of the twoangles from just one point on the shadowing pleniron surface, anintegration over the shape of the shadowing pleniron in θ and ϕtransferred to the subject surface ultimately results in an energysurface as provided herein and FIG. 25 . This surface is shown for 0varying between 0 and

$\frac{\pi}{2}$

and for ϕ from 0 to π (although it is repetitive in the symmetry of thearray layout—e.g., hexagonal lattices will have ϕ variations every 60degrees and rectangular only every 90).

Note that part of the above discourse, as example, and for simplicity,was for hemispherical plenirons. As has been noted herein, any plenironneed not be hemispherical but can adhere, for design optimization, tothe criteria set forth. Non-hemispherical plenirons will still work foreither the prior patent (as noted previously), or in the currentcontent, by adhering to the rules of design such as the Grand Ratio forcross-sections of a given device. Therefore, if other shapes, such asinverted paraboloids, partial solid ovals, gaussians, or other repeateddistribution, adhere, in most or all of its cross-sections, to thedesign rules specified, then it will be optimized as described. Anexample of a Gaussian-type of pleniron that may meet, depending on thematerial system, optimization is shown in and described with respect toFIG. 33 below.

The above described effect, from a simple arrangement of plenirons in aplenistell of arbitrary extent, can provide more detailed information ifthe source is coherent and monochromatic, for example per the discussionherein. Laser illumination can allow an array to detect power or currentvariations from changes in the orientation of the polarization of thefields. It should be noted, however, that the detection of thepolarization vector can also be modulated by the azimuthal andaltitudinal effects indicated herein. The sensitivity to thepolarization comes naturally from the regular arrangement of plenironsand because that arrangement does not vary in the Z direction. Thus,E-fields oscillating with a component parallel to the Z axis caninteract with structure sidewall edges differently than fields withcomponents parallel with the substrate plane.

It should be noted, for instance from the discussion herein, that apleniron, and particularly an array of plenirons in a plenistell, is avolumetric light capturing device. This is illustrated by example inFIG. 30A where, if a femtosecond-range pulse of light is impingent, aΔt_(γ1) is the “time-lag” represented by a packet of photons penetratingon the “top” of a pleniron versus the signal generated from a packetthat enters the pleniron “base” (near the substrate).

FIG. 30A is an isometric wireframe view of two separate photon packets,γ₁ and γ₂, where one packet intersects, with the ray as shown, the outertransparent conductor contact near the pleniron top, while the latterintersects the surface near the base. Note that in this figure the basedimensions of the pleniron layer dimensions (R_(C), d₂, d₃) are shown tobetter indicate the optically dense “absorber” layer immediately overR_(C) with thickness (at the base) dz. Note that γ₁ proceeds outside ofthe structure at first at speed v₁=c (speed of light in vacuum) but thenslows in the transparent conductor with the refracted ray shown. γ₁further advances upon near certain probability of acceptance into theoptically dense absorber layer (with index of refraction n₂). In FIG.30A the path taken in the absorber is shown as a helical “spiral” whichrepresents the average path taken by the Poynting vector of the photonensemble as it is wave-guided towards the bottom. Note that the figureindicates that the speed of the light in the absorber material will bec/n₂, and thus much slower than c. Therefore, the path taken by γ₁, dueto the lengthy waveguide path, exacerbated by the medium's highrefractive index, means that there is a very significant time differentbetween signals detected at the base from packets of photons impingingon the top versus those on the bottom. FIG. 30B, also representing thissituation, albeit in 2D (from the side), is a cross-section in the planeof incidence of the light rays γ₁ and γ₂, which is shown as x′.

This variation occurs because, when viewed from a small photon ensemble,or single photon, perspective, any light that enters first will be“waveguided” by the high index of refraction semiconductor, which slowsthat light prior to absorption. Because of the time differential fromeither single, interval, or periodic pulses, the device retains ahistory of these time-domain variations. Similarly, since the device is3-dimensional, light between structures is not attenuated, but begins tobe so upon entry into a structure. These factors allow a 3-dimensionaldevice such as this to retain real 3-dimensional information fromvarying light sources.

The retention of time-domain information about light variations throughthe optical depth of the device allows especially a regular arrayplenistell to capture and relay, in an informationally meaningfulfashion, 4-dimensional data. This is because, in part, any lightincident on the regular array from an azimuthal and altitudinal compoundangle can have a decodable additional periodic variation due to a pulsewavefront impinging on the “bottom” part in Z before the

$h + {\frac{c}{t}\sin\theta}$

“top” part of the puls impinges. Here, h is the pulse “height”, c is thespeed of light in a vacuum, t is the time lag, and θ is the compoundangle of incidence. The angle is deemed compound here since thesituation represented here obeys the aforementioned effects of spacingperiodicity as discussed herein.

For purposes of nomenclature, it will be noted that an array ofplenirons, in a plenistell, as described herein can be referred to as a“Block” action sensor. This naming in no way diminishes or limits itscapability, but only allows its unique features to be distinguished fromother aspects in the foregoing description.

In another embodiment, further information can be obtained from aregular array, if, as shown in FIG. 31 , a plenistell array is made suchthat each pleniron is individually “addressed” with a matrix of vias andlateral conductor lines in separate electrically isolated lines in X andY respectively. Note that the example in FIG. 31 is referred to asDirect Addressing, where each individual device has its own conductingline where a circuit is completed, as shown, to a common ground. On anydevice, whether digital or otherwise, the number of conducting lines ofan m×n integer number array necessary can be m*n. This is ordinarilyconsidered to be an excessive measure and misuse of valuable spacewithin or under a device. This has led to various schemes beingdeveloped that only require m+n lines. Note that FIG. 31 shows rows andcolumns as indexed J and K, respectively, since this makes themdistinct, in rows and columns from the underlying conductors labeled Mand N. Direct addressing is one methodology by which a matrixed devicecan provide data fast enough to measure the changes in lightconfiguration from plenirons over a plenistell in real time. Since apleniron, however, is not a digital device, and an array thereof iscapable of encapsulating an enormous amount of information in both timeand frequency domains, the integers m and n need not necessarily need beparticularly large. Even with direct addressing, as will be discussed infurther detail below, there will be a variable computable time lag forsignals from different plenirons within an array. Given the knownaddress, though, these conduction-path time lags can be accounted foralgorithmically.

It should be noted that reasonably sized, practical plenistells can bebuilt and grouped, for example, with known gap distances between them.The gap distances can also be used in an algorithm to spatially,temporally, and chromatically “de-gap” or “re-group” an array of arrays.The device space allowed by these designed-in gaps allows for somepre-processing circuitry as well as wide regions where coded groupedsignals can be transferred with wider and more conductive lines forexample following an analog-to-digital converter (ADC) and then groupingbits in accordance with a defined protocol. If the precision of directaddressing is necessary for very large information sets there is nodetriment to spacing plenistells in repeatable, wider arrays themselves,which then are also plenistells in their own right. A more commonexperience example of this is the use of multiple primary mirrors in areflector telescope or many radio dishes together in a Very Large Array(VLA).

Based on the design data, from material system as well as other factorsas set forth in Table 1 above, the pleniron outer extent size (diameter)would typically be in the micron to tens of microns range. Note thatwith very high quality semiconductors, as well as those with conducivedielectric functions and perhaps indirect band gaps (i.e., c-Si), thesizes of the individual devices could reasonably reach over 100 microns.This is mentioned here to provide an indicator, given the size range ofconducting lines via lithography with contemporary technology, thatsub-substrate layers or substrate backsides can provide space for agreat many conducting lines which are suitably isolated to avoidelectromagnetic “crosstalk”. The pleniron size ranges, especially withthe best semiconductor choices for high precision, are more thansufficient to allow conduction line layering to be a rather ordinaryengineering problem.

The lag times and ensuing complexity associated with an indirectaddressing scheme, such as those used in an erasable programmableread-only memory (EPROM) or Flash Memory array, can still allowdecodable volumetric information from each individual pleniron in aplenistell to provide more information than any current device.Decoding, although potentially more complicated, can still provide vastamounts of information for most, if not all, of the embodimentsdescribed herein.

When accounting for conduction time differences in the matrix of lines,any Matrix-Addressed plenistell provides information from the individualplenirons capable of discerning distinct and unique time-separatedevents in 4 dimensions. True time-of-flight, intensity, chromaticity,polarization, and spatial variation information, for full 4-dimensionaloptical object reformation is available from this device. Contrast thiscapability, for reference, with a planar-style photodetector, array orotherwise, which has no real Z-axis variation and thus no capability toretain temporally spaced events simultaneous with their spatialcounterparts.

The above described embodiment, for purposes of nomenclature, can bereferred to henceforth as a “Matrixed” or “Addressed” type ofplenistell. The two names, however, are not necessarily interchangeable.Being a “Matrixed” type of plenistell means that some method ofelectrically connecting each individual pleniron in such an array hasbeen done. Typically, this will be a regular layout of conducting linesthat are electrically insulated so that each individual pleniron has itsown individually selectable detector circuit. This may or may not bedone using the set of basis vectors referred to in the above discussion.Indeed, this might be the simplest way to provide individual addressesto each pleniron. “Matrixed” indicates a physical arrangement ofelectrical connection, while an addressing scheme does not have tofollow a coordinate system or even the physical arrangement ofconductors. It could be coded separately and independent of the physicallayout through software manipulation. Indeed, an “Addressed” plenistellcan even have layers of interconnects that have a third, fourth, ormore, layers of conductors and vias, for selecting individual plenironsin laid-out regions stressed with more importance.

In another manner by which more information can be gleaned from aregularly spaced and organized pleniron array, or plenistell, standardmethods of transferring electric potential and current can be used torotate one or more around a chosen axis. It is noted that anycombination of axes of rotation or combination of rotations andtranslations may be used as they may provide additional information froma specific detection setup or utilization. As a specific example, asingle axis rotation at a constant angular velocity, with a regularperiod, can be used in conjunction with the periodicity of the regularplenistell basis vector set, to provide even more information, withfewer unknowns or more variables, in either a Block or Matrix-Addressedarrangement. For further example, as introduced in FIG. 32 , a Gaussian,point, or plane wave source is translating in either a line or morecomplex “orbit” relative to a plenistell detector array (here, it isMatrix-Addressed). Because of real time comparison, on a pleniron level,between the changes to the time varying current at various addresses dueto the inherent azimuthal/altitudinal structurally-based factors withthose from an expected variation due to a 2*Pi periodicity fromrotation, a spinning plenistell detector array ameliorates or negatesunknowns from source distance and movement.

Because a rotating plenistell Matrix-Addressed array detector iscreating an independent non-inertial reference frame that transcendsLorentz transformations, it is able to utilize all of the aspects abovesynergistically to even detect source accelerations or complex changesin movement relative to a plenistell axis. This detection ability isindependent of additional capability to simultaneously detect time-basedsource “on/off” events or virtually any aspect of source or sourcesvariation.

The plenistell, whether rotating, or otherwise, as well as Block orMatrix-Addressed, has inherent color, or chromaticity, detection abilitythat is independent of its spatially and temporally varying sourcedetection. Referring back to Table 1 and the related discussion, we seethat the geometry, including the layer thicknesses, for the appropriatedegree of waveguiding and cavity resonation, as well as spacing andaccompanying occlusion, are determined partially at the outset ofdesign, by the selection of material system, i.e., the absorbersemiconductor being polysilicon or Ga—As or CIGS, etc., due to its bandgap, index of refraction, and extinction coefficient (which are allfunctions of wavelength over the range of absorption. These parts of theelectronic structure of the material and its dielectric functiondetermine a range of the physical parameters mentioned that will resultin a set of optimal device detection characteristics. These contributeto one metric indicated herein. For this discussion the quantity inparentheses in the equation in this section can be referred to as the“Grand Ratio”, and Eqn. 1 herein, which due to the inverse Sinefunction, only allows closer to optimal absorption at Grand Ratios (orGRs) that are <1. Any GR greater than 1, as determined by the physicallayer and core measurements, produces an expression in the parenthesesresulting in an angle, θ_(in), which can only have purely imaginarynumber solutions. Structures which optimally absorb the light within therange of the chosen semiconductor's electronic band gap range will havethe GR<1 so that the angle solution, θ_(in), is a real-valued number.These relations between optimal absorption and the semiconductor,expressed in a simple relationship such as GR, applies to the discussionof not only broad range absorption but also unique detection of spectralinformation by a pleniron, and plenistell detector.

It should be noted that the relatively simple metric of GR may alsoitself vary within a single pleniron since not only can one with a corehave such that varies from spherical, and the accompanying layers arenot conformal, but a pleniron made from underlying back-contact topologycan also be made such that it varies from spherical and conformality.These variations in GR can be suitable when provide better values atdifferent Z-direction heights in a pleniron. A Gaussian-shaped pleniron,for example created as a result of a topographical back contact with aconducive imprinting process, is shown in FIG. 33 . Note that twoseparate arbitrary example cross sections are taken (A and B) where GRvaries but remains solidly <1. These are taken at, again, arbitrarylevels of z, such as z=z₁ and z=z₂. These A and B cross-sections areshown as insets with their corresponding standard parameters, such asR_(C), d₂, and d₃.

The aforementioned electronic band gap of the chosen semiconductor(material system), is the distance in energy and momentum “space”,following Fourier transforms, between the valence band, full ofavailable electrons, and the conduction band, where the electrons mustbe elevated to contribute to conduction. In the chosen materials system,dopants, or controlled amounts of selected impurities, can be added toallow additional available electrons closer in energy space to theconduction region mentioned above. This electronic band gap, eitherintrinsic material, or with dopants, is the ultimate “arbiter” of thelongest wavelength (least energetic) photon or more “reddish” coloractually produces electrical current rather than heat. In somesemiconductors the band gap energy translates into absorption abilitywell into the infrared range such as with crystalline Si.

One example mechanism by which a pleniron detects color is through itsgeometry, such as in the layer thicknesses, the core size and shape, andthe ratios of the same. Note, however, that the GR of a given structurealso depends on its refractive indices, which is the real part of thesquare root of the dielectric function, which varies by its dispersionrelation across its useful electronic absorption range. The imaginarypart of the square root of the complex, and spectrally varying,dielectric function is the extinction coefficient, k. This willdetermine the distance that a wave, as a function of wavelength, willtravel in the semiconductor material once it is trapped by the optimizedgeometry. Since the pleniron structure, as outlined herein, allows thesemiconductor, due to its higher real-valued refractive index, towaveguide light, and act as an annular cavity resonator, wavelengths oflight with lower k values, typically according to the dispersionrelation, longer, or more red regions of the spectrum, will travelfurther prior to absorption. Shorter wavelengths near the UV-range willabsorb very quickly and may not waveguide at all, being absorbed beforeeven reaching a reflective back surface of the annulus. Therefore, bluerareas of the spectrum can have far less angular dependence and will actupon either a pleniron alone, or especially upon a regularly spacedplenistell, more as an angled flat or planar surface. The lack ofangular dependence in this range can be true for both azimuthal oraltitudinal dependencies.

It should be noted that the lack of angular dependence for blue light istrue for the structure and array under consideration in the discussionabove. Although for said structure the lack of blue-range angulardependence, along with its unique electronic signature, aids in thecolor identification, a different structure, with different geometry anda requisite material system, optionally can accompany the above toobtain complex angular dependencies in the blue or ultraviolet range aswell.

It would not only be the angular dependence, in multiple directions, andwith polarization variation, that would identify the spectral range ofincident light, but also electronic factors unique to that range.Regardless of the quality of a given semiconductor system, there willalways be equivalent resistances in a detector circuit representingelectron-hole recombination. When a photovoltaic device generates anelectric current from photons, an exciton is created in the device'sdepletion region. For charge conservation reasons the exciton is aquasi-particle that represents during its lifetime both an electron anda hole. These are provided enough energy by the incident photon toescape the valence band, be accelerated oppositely each other by thedepletion zone field, and eventually enter the front or back electricalcontact. The incident photon energy, however, also determines theexciton's total “leftover” kinetic energy. Although a pleniron, as shownin FIG. 9 , has the distinct advantage of a long optical path via theannular waveguide, but a short electrical path as determined by theconformal PN junction due to the layers and the resulting depletion zoneelectric field, shorter wavelength photons will have less likelihood ofbeing recombined through collisions simply because they are energeticenough to exit the semiconductor quicker. This results in voltagechanges across the junction due to equivalent parallel shunt resistance,as well as a series resistance as a direct voltage drop. These are easyto detect with angular variation in altitude given a lone pleniron, andboth altitude and azimuth periodicities given a regular plenistell. Allwavelengths in the dispersion relation range of the electronic band gapwill have different series and shunt resistances and accompanyingdependencies on all compound angles and periodicities due to the effectsmentioned in the above discussion. The color-detection ability, throughthese factors, will be accentuated if a plenistell is Matrix-Addressedas well as outlined above.

In another embodiment, a Matrix-Addressed plenistell made up ofplenirons which are intentionally made to be geometrically not optimizedfor light trapping and therefore have GRs of >1 can be considered.Furthermore, the junctions in these Matrix-Addressed plenirons can beengineered such that they are reversed photovoltaics, and therefore actas Light Emitting Diodes (LEDs). Since the GR is variable depending onunderlying core or structured substrate variations from spherical aswell as accompanying layer changes, a pleniron array of light emitterswill vary widely from planar LED behavior. This is primarily because,even with lossy GR structures at or near above 1, the structure stillwaveguides and resonates, it just does so while “leaking” light in areasideal for the electromagnetic mode and index-shifted wavelength at thatexit “site”.

As outlined herein, the pleniron, and especially its regularly arrangedplenistell, is a true absorber of 3D electromagnetic information with anaccompanying temporal component. Therefore, a specifically designedplenistell, from regularly spaced plenirons designed with GRs around andabout 1, will be lossy waveguide resonators which similarly “leak” lightinto intended spectral ranges and specific angular directions. Such aplenistell, which is Matrix-Addressed as above, would be a true 3D EMimage re-constructor. These effects can be dependent on the array beingprovided, via its Matrix-Addressing, an appropriately coded set ofelectrical signals that could excite the modes necessary for such 3Dimagery. These can originate, in conceptions of the excitation, forexample, as back contact signals that contain modes of frequencyexcitation using the core or back-contact structure as a form ofantenna. The modal frequencies at the surface or interface of the backcontact and the semiconductor instigate variable excitation along theannular PN junction. The light produced from the annular diode will thenwaveguide and resonate in a form similar to how it would have otherwisedone as a light absorber. As indicated above, however, since thisembodiment is for a release of full 3D imagery in a very wide solidangle over a properly configured plenistell, the layers and core areengineered specifically in accordance with Eqn. 1 herein to obtain GRsnear and/or about 1. The physical layer thicknesses, core diameter, andaccompanying material system can be designed in this case to “leak”light at a specifically engineered rate in the correct spectral rangesto allow the formation, from applicable code, of a full 3D image in thewidest possible solid angle. Some of these concepts are illustrated inFIG. 34 .

FIG. 34 shows a pleniron of an approximately spheroidal toinverted-parabolic outer shape in two separate cross-sections. Each ofthese cross-sections shows light leakage from separate types of modes.Here, the cross-section is viewed as at least partiallycylindrical-to-hemispherical geometry that leads to Bessel functionsolutions radially, Hankel-variants azimuthally, and rough sinusoidsaxially, where the term “axial” is used very loosely. In each case thewaveforms shown in example are indicative of their respective form oflight “leakage”. Note that in the upper cross section, shown in the x-zplane, the “axial” rough sinusoids are shown leaking with example “rays”coming out in various directions. Here, some arbitrary cross sectionsare taken to show that example GRs are at, about, or >1. Note that thetypical geometrical methodology for measuring GR is provided in R_(C),d₂, and d₃. This cross section is shown, in this same figure,transferred by projection to the x-y plane. Here there are three groupsof example waves “leaking” from their modes. Group A is a high frequencyexample azimuthal wave approximated by leaky Hankel-variant functions.The “leaks” are shown as “random” rays from the transparent conductorouter surface. The frequency of the azimuthal wave in this example isν=ν_(A). Lower frequency, with ν=ν_(C), are shown as part of Group C.These are, likewise, leaking EM from the TCO surface. Group B includesradial modes of increasing frequency with ν=ν₁, ν₂, ν₃ at the 3 lowerquadrants of the cross-section. These, as mentioned, are modified leakyBessel-type functions.

It should be noted that the degree to which a pleniron will leak lightis a complicated function dependent on spectrum, geometry, electronicconsiderations, dielectric function, and more. As a general rule,however, the further that the GR of a cross-section is from being GR>1,the more, exponentially, is the rate at which light at all wavelengthswill exit a given cross section of outer surface.

The current embodiment under discussion can leads to the plenistelldetector, which is Matrix-Addressed, and is the subject of discussionherein to act as an “encoder” of the real and complete 3D image datanecessary for the image creation ability of the “lossy” plenistell asdiscussed herein and with respect to FIG. 34 . That is, theMatrix-Addressed plenistell, which could otherwise be used as either ageneral purpose detector of a wide range of data or as a specificdetector for whatever custom use an end-user requires, would here,specifically, be utilized as a detector to build an image coding thatcould be stored, digitally or otherwise. Therefore, the plenistell thatobtains the involved data has plenirons in a regular array that have GRsof <1, while the plenistell that projects, casts, or releases the codeddata, in Matrix-Addressed form, will have plenirons that have GRs nearor about 1. This concept is incompletely analogized by referring to thecapturing plenistell as a “camera”. The rationale for the incompletenessof the summary is that a camera's detection apparatus usually comprisesa pixel array of which each is a planar device that lacks the volumetriccapacity or Optical Volume and time-based capture of a plenistell.Hereafter, for simplicity, a plenistell with the aforementionedcharacteristics to be used for capturing full 3D image data for digitalstorage can be referred to as a “plenera”.

Although in general the optical characteristics of the beginning basicdesign of a plenera are simplified in the GR key metric, the electroniccharacteristics are mostly characterized around the dielectric function,electronic band gap, and the electronic (exciton) mean-free path acrossthe useful spectrum. As mentioned above in multiple sections, theselection of the material system, as per Table and related discussion,determines the range of light that is not only absorbable, but thatrange that optimally captures, waveguides, resonates, and converts thelight into electronic signals (excitons). The dielectric function, asmentioned, contains the index of refraction, n, and the extinctioncoefficient, k, which together determine the range of light whichrequires and allows the useful path length in the annular absorber toallow the resonation and guiding of waves as previously shown. The otherfactors were sufficiently described herein.

It should be mentioned that image data captured and stored by a plenera,whether digitally or in some other form, can also be transmitted, in anymeans available in the current art, such that it can be decoded andprojected, cast, released, or otherwise viewed by a “lossy” plenistellas previously described herein. To understand the ramifications of the“projection” capability of such a plenistell, hereafter, for thisembodiment, referred to as a “plenicast”, one can imagine what anarbitrary viewer, on the receiving end, would observe. If, for example,a plenera captures, obtains, and stores full 3D imagery of a person who,for this example, would be taking up a large part of the solid angle ofreceptivity of the plenera, the 3D image data would be shown by the“plenicast” in a similar 3D fashion across its engineered lossy solidangle of “projection”. Therefore, an image recreated by the plenicastwould not be limited to the solid angle subtended by the physical sizeof the plenicast such as from a screen or objective at a distance, butwould appear, due to its coding of the 3D data, as the person in totalfrom whatever angle from which the observer happens to be. In otherwords, if an observer, on the receiving end, happens to be viewing fromdirectly behind the plenicast, they would see an image of the personfrom the front, along with any nearby background or “near-ground” 3Dimagery such as a stool or other furniture, etc. Moving outwards fromthis location, albeit not obstructing or obscuring the plenicast, onewould see more of the side of the person and accompany objects or“near-ground”. It is clear that such movement will affect the quality ofthe 3D image, as it is likely that color and intensity would diminish invarious angular ranges and with distance. Methodologies to rectify thisproblem might include transmitting a full 3D image of the person from anearly coaxial plenera, but using one with altered imaging qualities,having been varied from the first by modification of the optical factorsmentioned in the preceding sections.

The imagery example in the previous section must be extended withcaveats and solutions, as required, by various end-users. For extendedexample, consider that the plenera capturing the person's 3D image hasonly limited optical data from the person's back side if they are facingthe plenera, as well as diminishing information about far oblique sides.The image from an observer viewing from in front of the plenicast wouldbe a rather bizarre view of the front of the person but only a frontal“shell”. Likewise, from the side one would view only the frontal shellcaptured by the plenera in front. All of these issues can be solved bytransmitting a combined signal from a set of pleneras positionedappropriately to capture the entire shell of the person and provide afull “solid” appearing “form”. Appropriate software could rectify anydecoding issues such that the image can be reconstructed by a severalplenicasts in total.

The embodiments under discussion herein naturally lead to anotherembodiment of the present invention by either actively or passivelyrendering a part of a cast or “projected” image as transparent orinvisible. Given that the discussion henceforth has been using plenerasand plenicasts, often in arrangements, the active methodology ofinvisibility will be discussed first. It should be noted that a subjectbeing ultimately viewed, such as the person in the previous examples,would view the image capturing plenera as a completely “void-like” blackfield of whatever shape. This is due to its near complete angular andspectral light capturing ability which virtually nullifies anyreflection. Given, however, the specifically engineered nature of theplenicast, a transmitted set of 3D image data could be altered on thesending and/or receiving end such that the person does not appear in theend image. Therefore, one side of an object could be covered in pleneraswhile the other side is strategically covered in plenicasts. The pleneraside can digitally encode the 3D imagery such that all of the plenicastson the opposite side are transmitted data to project 3D imagery from theback to the front. This would effectively make the object invisible inwhatever wavelength range desired through manipulation of the materialsystem and accompanying optical and electronic factors.

Another embodiment encompasses the passive invisibility mentioned above,but more generally. If one envisions a plenistell, with light capturingplenirons, as designed per the requirements herein, but with eithertransparent or semi-transparent bottoms or bases. This concept isfurther illustrated in FIG. 35 . Here, the typical geometricconsiderations are shown for GR as well as some example rays that passthrough the base of the pleniron absorber annulus (in the width of d₂)and refract into the lower refractive index material underneath (hereacting as the substrate). In this embodiment it is most desirable toutilize a high index material as the annulus waveguiding materialpreviously in place as the absorbing material layer and/or core. Itwould be sufficient to have a high index material that has a very highpath length for all but the shortest wavelength in its electronic bandgap range. An example would be crystalline silicon (c-Si) because of itsdielectric function encompassing a fairly low extinction coefficient, k,for most of the visible spectrum. Depending on the sizes of theplenirons involved, most the waveguided light would resonate within theannulus but be, again, “leaked”, albeit this time from the base orbottom. If these bases were coupled optically to either standard opticalfibers (although this is difficult on the scale of the plenirons giventheir area number density) or into a flat dielectric waveguide, then the3D information could be transmitted optically in its entirety and thusskipping the encoding and decoding steps provided in the activeembodiments above. Note that the figure repeats some explanation ofthese refractive index requirements.

In the embodiment under discussion a plenistell that wholly captureslight over virtually all wavelengths and angles (and thus is black whenviewed from above), when coupled to a flat waveguide plate, or flexiblewaveguide “ribbon” or “sheet”, would passively transmit the whole andcomplete 3D image information optically to a single or set of “lossy”plenistells in some other location. If the flat waveguide were flexibleand turned around to the other side of an object, as shown in theexample provided in FIG. 36 , the “lossy” plenistell would project,cast, or release full 3D imagery on the other side of the object,thereby rendering it completely invisible. This invisibility can beachieved in whatever ranges of wavelengths desired by the designer whenthey are considering material sets, sizes, layer thicknesses, GRs, andall of the other considerations provided herein.

The plenistells mentioned in the foregoing paragraph, for capturing andrecreating a full 3D image through the use of such with GRs varying from<1 on one side versus near and about 1 on the other, are not limited inthis embodiment to the rendering of an object invisible. The ability tocapture a full 3D image and recreate it in another location passivelythrough the use of a flexible waveguide can also clearly be used forHead Up Displays (HUDs), as well as extremely thin and light opticalcoupling devices for displaying full 3D information on typical opticalviewable surfaces. Examples of this would be to transmit or castpassively 3D imagery onto the inside of sunglasses, eyeglasses, visors,contact lenses, retinas, or almost any other conceivable opticalsurface.

In yet another embodiment of the current invention a plenistell could beused, in a manner similar to FIG. 35 and/or FIG. 36 , to direct lightcollected from virtually all directions (as has been established in itsentirety in this discourse) into an optical cavity. This could be forthe purposes of optical memory storage or for optically pumping a lasingmaterial such as a crystal, gas, or plasma.

Although the claimed subject matter has been described with a certaindegree of particularity, it should be recognized that elements thereofmay be altered by persons skilled in the art without departing from thespirit and/or scope of claimed subject matter. It is believed that thesubject matter pertaining to a sensor comprising photovoltaic device andmany of its attendant utilities will be understood by the forgoingdescription, and it will be apparent that various changes may be made inthe form, construction and/or arrangement of the components thereofwithout departing from the scope and/or spirit of the claimed subjectmatter or without sacrificing all of its material advantages, the formherein before described being merely an explanatory embodiment thereof,and/or further without providing substantial change thereto. It is theintention of the claims to encompass and/or include such changes.

What is claimed is:
 1. A sensor, comprising: a photovoltaic device,wherein the photovoltaic device comprises: a core having a shape that isat least partially spherical; an absorber disposed over the core andhaving a shape that is at least partially curved; and a transparentconductor disposed over the absorber and having a shape that is at leastpartially curved; wherein the transparent conductor has an index ofrefraction that is less than an index of refraction of the absorber suchthat the transparent conductor and the absorber function as a lens torefract impinging photons into the absorber; wherein an interfacebetween the transparent conductor and the absorber has a smoothnessdefined such that a distance between peak to peak features on a surfaceof the transparent conductor at the interface is less than about onetenth of a wavelength of the impinging photons divided by the index ofrefraction of the transparent conductor; and wherein the absorber andthe transparent conductor have indices of refraction and thicknessesselected to function as an annular waveguide such that the photonsimpinging into the absorber travel circumferentially in the absorberabout a center of the core.